Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1252 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 163 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #20289120 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20285168 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20285167 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #20274005 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | #20273306 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C53×#1525 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×#13133245 | — | 2 | 4 | no | — |
| 8 | C2×#13133242 | — | 2 | 2 | no | — |
| 9 | #16811365 | C22 | 1 | 4 | yes | complemented |
| 10 | #16811339 | — | 2 | 1 | no | — |
| 11 | #16811338 | — | 2 | 2 | no | — |
| 12 | D4×D212 | — | 2 | 2 | no | — |
| 13 | #16811258 | — | 2 | 1 | no | — |
| 14 | #16811189 | — | 2 | 4 | no | — |
| 15 | #16811187 | — | 2 | 2 | no | — |
| 16 | #16811173 | C22 | 1 | 2 | yes | — |
| 17 | C2×#13133214 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | #16811013 | C22 | 1 | 4 | yes | complemented |
| 19 | #16811012 | C22 | 1 | 8 | yes | complemented |
| 20 | #16811000 | — | 2 | 2 | no | — |
| 21 | #16810999 | — | 2 | 1 | no | — |
| 22 | #16810997 | — | 2 | 1 | no | — |
| 23 | #16810996 | — | 2 | 2 | no | — |
| 24 | C4×#11719917 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | #16810362 | C22 | 1 | 8 | yes | complemented |
| 26 | C53×#532 | C22 | 1 | 1 | yes | characteristic |
| 27 | C4×M16×C53 | C22 | 1 | 2 | yes | complemented |
| 28 | C53×#329 | C22 | 1 | 4 | yes | complemented |
| 29 | C2×#11719945 | D4 | 1 | 4 | yes | — |
| 30 | C22×D212 | — | 2 | 2 | no | — |
| 31 | C22×D212 | — | 2 | 1 | no | — |
| 32 | C22×D212 | — | 2 | 2 | no | — |
| 33 | C2×D4×D53 | — | 2 | 4 | no | — |
| 34 | #13133245 | — | 4 | 16 | no | — |
| 35 | #13133242 | — | 4 | 8 | no | — |
| 36 | C2×#11719913 | — | 2 | 8 | no | — |
| 37 | C2×#11719924 | — | 2 | 4 | no | — |
| 38 | C2×D424 | — | 2 | 8 | no | — |
| 39 | C2×#11719922 | — | 2 | 4 | no | — |
| 40 | C2×#11719917 | — | 2 | 1 | no | — |
| 41 | #13133217 | D4 | 1 | 2 | yes | — |
| 42 | #13133214 | — | 2 | 2 | no | — |
| 43 | #13133214 | — | 2 | 1 | no | — |
| 44 | #13133214 | D4 | 1 | 2 | yes | — |
| 45 | #13133214 | C23 | 1 | 2 | yes | — |
| 46 | #13133213 | — | 2 | 4 | no | — |
| 47 | #13133206 | — | 2 | 4 | no | — |
| 48 | #13133205 | C23 | 1 | 4 | yes | — |
| 49 | #13133203 | — | 2 | 8 | no | — |
| 50 | #13133192 | — | 2 | 4 | no | — |
| 51 | #13133191 | — | 2 | 4 | no | — |
| 52 | #13133191 | — | 2 | 2 | no | — |
| 53 | #13133191 | — | 2 | 2 | no | — |
| 54 | #13133188 | — | 2 | 4 | no | — |
| 55 | #13133187 | — | 2 | 8 | no | — |
| 56 | #13133185 | — | 2 | 4 | no | — |
| 57 | #13133185 | — | 2 | 4 | no | — |
| 58 | C4×D212 | — | 2 | 2 | no | — |
| 59 | C4×D212 | — | 2 | 2 | no | — |
| 60 | #13133176 | — | 2 | 2 | no | — |
| 61 | #13133175 | — | 2 | 4 | no | — |
| 62 | #13133128 | C23 | 1 | 2 | yes | — |
| 63 | C4×#88322 | — | 2 | 1 | no | — |
| 64 | C2×#41×C53 | D4 | 1 | 2 | yes | — |
| 65 | C2×M16×C53 | — | 2 | 2 | no | — |
| 66 | C4⋊Q8×C53 | D4 | 1 | 1 | yes | characteristic |
| 67 | #127×C53 | D4 | 1 | 1 | yes | characteristic |
| 68 | #124×C53 | C23 | 1 | 2 | yes | — |
| 69 | #121×C53 | — | 2 | 2 | no | — |
| 70 | C4×D4×C53 | — | 2 | 2 | no | — |
| 71 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 72 | #97×C53 | C23 | 1 | 4 | yes | — |
| 73 | C4×C8×C53 | — | 2 | 2 | no | — |
| 74 | C23×D53 | — | 2 | 4 | no | — |
| 75 | C23×D53 | — | 4 | 1 | no | — |
| 76 | #41×C53 | — | 4 | 4 | no | — |
| 77 | C2×Q8×C53 | C2×D4 | 1 | 2 | yes | — |
| 78 | C2×D4×C53 | — | 2 | 2 | no | — |
| 79 | C2×D4×C53 | — | 2 | 2 | no | — |
| 80 | C2×D4×C53 | C2×D4 | 1 | 2 | yes | — |
| 81 | C22×C4×C53 | — | 2 | 2 | no | — |
| 82 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 83 | C22×C4×C53 | C2×D4 | 1 | 2 | yes | — |
| 84 | C2×C22⋊D53 | — | 2 | 8 | no | — |
| 85 | C2×C22⋊D53 | — | 2 | 4 | no | — |
| 86 | D4×D53 | — | 8 | 8 | no | — |
| 87 | #11719945 | — | 4 | 8 | no | — |
| 88 | C2×D212 | — | 2 | 2 | no | — |
| 89 | C2×D212 | — | 2 | 2 | no | — |
| 90 | C2×D212 | — | 2 | 2 | no | — |
| 91 | C2×D212 | — | 2 | 4 | no | — |
| 92 | C2×D212 | — | 2 | 4 | no | — |
| 93 | C2×D212 | — | 4 | 4 | no | — |
| 94 | C2×D212 | — | 4 | 8 | no | — |
| 95 | C2×D212 | — | 4 | 2 | no | — |
| 96 | C2×D212 | — | 4 | 1 | no | — |
| 97 | C2×D212 | — | 8 | 4 | no | — |
| 98 | C2×D212 | C2×D4 | 1 | 4 | yes | — |
| 99 | C2×C4×D53 | — | 2 | 4 | no | — |
| 100 | C2×Dic106 | C2×D4 | 1 | 4 | yes | — |
| 101 | M16×C53 | — | 2 | 8 | no | — |
| 102 | C2×C8×C53 | — | 2 | 4 | no | — |
| 103 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 104 | C22⋊C4×C53 | — | 2 | 4 | no | — |
| 105 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 106 | C42×C53 | C2×D4 | 1 | 2 | yes | — |
| 107 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 108 | C22⋊Dic53 | — | 2 | 4 | no | — |
| 109 | #11719924 | — | 4 | 8 | no | — |
| 110 | #11719922 | — | 4 | 8 | no | — |
| 111 | #11719921 | — | 2 | 8 | no | — |
| 112 | #11719921 | — | 2 | 4 | no | — |
| 113 | #11719921 | — | 2 | 4 | no | — |
| 114 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 115 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 116 | C4×Dic53 | — | 2 | 4 | no | — |
| 117 | #11719917 | — | 2 | 4 | no | — |
| 118 | C2×#88322 | — | 2 | 2 | no | — |
| 119 | D424 | — | 4 | 16 | no | — |
| 120 | #11719913 | — | 4 | 16 | no | — |
| 121 | C23×C53 | — | 2 | 2 | no | — |
| 122 | C23×C53 | #120 | 1 | 1 | yes | characteristic |
| 123 | C22×D53 | — | 2 | 4 | no | — |
| 124 | C22×D53 | — | 4 | 2 | no | — |
| 125 | C22×D53 | — | 8 | 4 | no | — |
| 126 | C22×D53 | — | 8 | 8 | no | — |
| 127 | C22×D53 | — | 8 | 4 | no | — |
| 128 | C22×D53 | — | 8 | 2 | no | — |
| 129 | Q8×C53 | — | 4 | 2 | no | — |
| 130 | D4×C53 | — | 4 | 2 | no | — |
| 131 | D4×C53 | — | 4 | 4 | no | — |
| 132 | D4×C53 | — | 8 | 2 | no | — |
| 133 | C2×C4×C53 | — | 2 | 4 | no | — |
| 134 | C2×C4×C53 | — | 2 | 2 | no | — |
| 135 | C2×C4×C53 | — | 2 | 2 | no | — |
| 136 | C2×C4×C53 | — | 4 | 4 | no | — |
| 137 | C2×C4×C53 | #120 | 1 | 2 | yes | — |
| 138 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 139 | C2×C4×C53 | C22×D4 | 1 | 2 | yes | — |
| 140 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 141 | C22⋊D53 | — | 8 | 4 | no | — |
| 142 | C22⋊D53 | — | 8 | 8 | no | — |
| 143 | C2×Dic53 | — | 2 | 4 | no | — |
| 144 | D212 | — | 4 | 4 | no | — |
| 145 | D212 | — | 4 | 8 | no | — |
| 146 | D212 | — | 4 | 4 | no | — |
| 147 | D212 | — | 4 | 4 | no | — |
| 148 | D212 | — | 4 | 4 | no | — |
| 149 | D212 | — | 8 | 4 | no | — |
| 150 | D212 | — | 8 | 4 | no | — |
| 151 | D212 | — | 8 | 2 | no | — |
| 152 | C4×D53 | — | 4 | 8 | no | — |
| 153 | Dic106 | — | 4 | 4 | no | — |
| 154 | C8×C53 | — | 2 | 8 | no | — |
| 155 | #88322 | — | 2 | 4 | no | — |
| 156 | #19073 | — | 53 | 1 | no | maximal, Sylow |
| 157 | C22×C53 | — | 2 | 2 | no | — |
| 158 | C22×C53 | — | 2 | 1 | no | — |
| 159 | C22×C53 | — | 4 | 4 | no | — |
| 160 | C22×C53 | — | 4 | 2 | no | — |
| 161 | C22×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 162 | C2×D53 | — | 4 | 4 | no | — |
| 163 | C2×D53 | — | 4 | 4 | no | — |
| 164 | C2×D53 | — | 4 | 4 | no | — |
| 165 | C2×D53 | — | 8 | 4 | no | — |
| 166 | C2×D53 | — | 8 | 2 | no | — |
| 167 | C2×D53 | — | 16 | 8 | no | — |
| 168 | C2×D53 | — | 16 | 4 | no | — |
| 169 | C4×C53 | — | 2 | 1 | no | — |
| 170 | C4×C53 | — | 2 | 2 | no | — |
| 171 | C4×C53 | — | 4 | 2 | no | — |
| 172 | C4×C53 | #453 | 1 | 4 | yes | — |
| 173 | C4×C53 | #453 | 1 | 2 | yes | — |
| 174 | Dic53 | — | 4 | 4 | no | — |
| 175 | #3549 | — | 53 | 1 | no | — |
| 176 | #3151 | — | 53 | 2 | no | — |
| 177 | #3151 | — | 53 | 1 | no | — |
| 178 | #1655 | — | 53 | 8 | no | — |
| 179 | #1525 | — | 53 | 2 | no | — |
| 180 | #1525 | D53 | 1 | 1 | yes | characteristic, complemented |
| 181 | C2×C53 | — | 4 | 1 | no | — |
| 182 | C2×C53 | — | 8 | 2 | no | — |
| 183 | C2×C53 | C2×#453 | 1 | 2 | yes | — |
| 184 | C2×C53 | C2×#453 | 1 | 1 | yes | characteristic |
| 185 | D53 | — | 8 | 4 | no | — |
| 186 | D53 | — | 16 | 2 | no | — |
| 187 | C2×AGL(1,ℤ/8) | — | 106 | 4 | no | — |
| 188 | C2×AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 189 | H(3,𝔽4) | — | 53 | 4 | no | — |
| 190 | #555 | — | 106 | 2 | no | — |
| 191 | #555 | — | 106 | 1 | no | — |
| 192 | D42 | — | 106 | 2 | no | — |
| 193 | D42 | — | 106 | 1 | no | — |
| 194 | #535 | — | 106 | 4 | no | — |
| 195 | #535 | — | 106 | 2 | no | — |
| 196 | #532 | — | 53 | 2 | no | — |
| 197 | #532 | C2×D53 | 1 | 1 | yes | characteristic |
| 198 | C2×#127 | — | 53 | 1 | no | — |
| 199 | #496 | — | 53 | 4 | no | — |
| 200 | #496 | — | 53 | 8 | no | — |
| 201 | #493 | — | 106 | 2 | no | — |
| 202 | #493 | — | 106 | 1 | no | — |
| 203 | #492 | — | 106 | 2 | no | — |
| 204 | #492 | — | 106 | 1 | no | — |
| 205 | C4×M16 | — | 53 | 1 | no | — |
| 206 | C4×M16 | C2×D53 | 1 | 2 | yes | complemented |
| 207 | #329 | — | 53 | 8 | no | — |
| 208 | #329 | C2×D53 | 1 | 4 | yes | complemented |
| 209 | C53 | #19073 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 210 | C2×#41 | — | 53 | 4 | no | — |
| 211 | C2×#41 | D212 | 1 | 2 | yes | — |
| 212 | C22×D4 | — | 106 | 2 | no | — |
| 213 | C22×D4 | — | 106 | 4 | no | — |
| 214 | C22×D4 | — | 106 | 1 | no | — |
| 215 | C22×D4 | — | 106 | 2 | no | — |
| 216 | AGL(1,ℤ/8) | — | 212 | 16 | no | — |
| 217 | AGL(1,ℤ/8) | — | 212 | 8 | no | — |
| 218 | C2×SD16 | — | 106 | 8 | no | — |
| 219 | C2×SD16 | — | 106 | 4 | no | — |
| 220 | C2×D8 | — | 106 | 8 | no | — |
| 221 | C2×D8 | — | 106 | 4 | no | — |
| 222 | C2×M16 | — | 2 | 2 | no | — |
| 223 | C2×M16 | — | 106 | 1 | no | — |
| 224 | C4⋊Q8 | — | 53 | 2 | no | — |
| 225 | C4⋊Q8 | D212 | 1 | 1 | yes | characteristic |
| 226 | #127 | — | 53 | 2 | no | — |
| 227 | #127 | — | 53 | 2 | no | — |
| 228 | #127 | — | 106 | 4 | no | — |
| 229 | #127 | — | 106 | 1 | no | — |
| 230 | #127 | — | 106 | 2 | no | — |
| 231 | #127 | D212 | 1 | 1 | yes | characteristic |
| 232 | #124 | — | 53 | 4 | no | — |
| 233 | #124 | — | 106 | 8 | no | — |
| 234 | #124 | — | 106 | 4 | no | — |
| 235 | #124 | C22×D53 | 1 | 2 | yes | — |
| 236 | #121 | — | 2 | 2 | no | — |
| 237 | #121 | — | 106 | 4 | no | — |
| 238 | #121 | — | 106 | 4 | no | — |
| 239 | #121 | — | 106 | 4 | no | — |
| 240 | #121 | — | 106 | 2 | no | — |
| 241 | #121 | — | 106 | 2 | no | — |
| 242 | #120 | — | 106 | 8 | no | — |
| 243 | #120 | — | 106 | 4 | no | — |
| 244 | #120 | — | 106 | 4 | no | — |
| 245 | C4×D4 | — | 2 | 2 | no | — |
| 246 | C4×D4 | — | 106 | 2 | no | — |
| 247 | C4×D4 | — | 106 | 2 | no | — |
| 248 | #117 | — | 106 | 4 | no | — |
| 249 | #117 | — | 106 | 2 | no | — |
| 250 | C2×C42 | C22×D53 | 1 | 1 | yes | characteristic |
| 251 | #97 | — | 53 | 2 | no | — |
| 252 | #97 | C22×D53 | 1 | 4 | yes | — |
| 253 | C4×C8 | — | 2 | 2 | no | — |
| 254 | C4×C8 | — | 106 | 1 | no | — |
| 255 | C24 | — | 106 | 4 | no | — |
| 256 | C24 | — | 212 | 1 | no | — |
| 257 | #41 | — | 4 | 4 | no | — |
| 258 | #41 | — | 212 | 8 | no | — |
| 259 | C2×Q8 | — | 53 | 4 | no | — |
| 260 | C2×Q8 | C2×D212 | 1 | 2 | yes | — |
| 261 | C2×D4 | — | 2 | 2 | no | — |
| 262 | C2×D4 | — | 2 | 2 | no | — |
| 263 | C2×D4 | — | 53 | 4 | no | — |
| 264 | C2×D4 | — | 106 | 4 | no | — |
| 265 | C2×D4 | — | 106 | 8 | no | — |
| 266 | C2×D4 | — | 106 | 4 | no | — |
| 267 | C2×D4 | — | 106 | 2 | no | — |
| 268 | C2×D4 | — | 106 | 2 | no | — |
| 269 | C2×D4 | — | 106 | 4 | no | — |
| 270 | C2×D4 | — | 106 | 2 | no | — |
| 271 | C2×D4 | — | 424 | 4 | no | — |
| 272 | C2×D4 | — | 424 | 8 | no | — |
| 273 | C2×D4 | — | 212 | 8 | no | — |
| 274 | C2×D4 | — | 212 | 4 | no | — |
| 275 | C2×D4 | — | 212 | 2 | no | — |
| 276 | C2×D4 | — | 212 | 1 | no | — |
| 277 | C2×D4 | C2×D212 | 1 | 2 | yes | — |
| 278 | C22×C4 | — | 2 | 2 | no | — |
| 279 | C22×C4 | — | 106 | 4 | no | — |
| 280 | C22×C4 | C2×D212 | 1 | 1 | yes | characteristic |
| 281 | C22×C4 | D4×D53 | 1 | 2 | yes | — |
| 282 | SD16 | — | 212 | 16 | no | — |
| 283 | SD16 | — | 212 | 8 | no | — |
| 284 | D8 | — | 212 | 16 | no | — |
| 285 | D8 | — | 212 | 8 | no | — |
| 286 | M16 | — | 2 | 8 | no | — |
| 287 | M16 | — | 106 | 4 | no | — |
| 288 | C2×C8 | — | 2 | 4 | no | — |
| 289 | C2×C8 | — | 106 | 2 | no | — |
| 290 | C4⋊C4 | — | 2 | 2 | no | — |
| 291 | C4⋊C4 | — | 106 | 2 | no | — |
| 292 | C4⋊C4 | — | 106 | 2 | no | — |
| 293 | C22⋊C4 | — | 2 | 4 | no | — |
| 294 | C22⋊C4 | — | 106 | 8 | no | — |
| 295 | C22⋊C4 | — | 106 | 4 | no | — |
| 296 | C22⋊C4 | — | 106 | 4 | no | — |
| 297 | C22⋊C4 | — | 106 | 4 | no | — |
| 298 | C42 | — | 106 | 4 | no | — |
| 299 | C42 | C2×D212 | 1 | 1 | yes | characteristic |
| 300 | C42 | D4×D53 | 1 | 2 | yes | — |
| 301 | C42 | C23×D53 | 1 | 1 | yes | characteristic |
| 302 | C23 | — | 2 | 2 | no | — |
| 303 | C23 | — | 106 | 4 | no | — |
| 304 | C23 | — | 424 | 4 | no | — |
| 305 | C23 | — | 424 | 2 | no | — |
| 306 | C23 | — | 424 | 8 | no | — |
| 307 | C23 | — | 424 | 4 | no | — |
| 308 | C23 | — | 212 | 2 | no | — |
| 309 | C23 | #13133187 | 1 | 1 | yes | characteristic |
| 310 | Q8 | — | 4 | 2 | no | — |
| 311 | Q8 | — | 212 | 4 | no | — |
| 312 | D4 | — | 4 | 2 | no | — |
| 313 | D4 | — | 4 | 4 | no | — |
| 314 | D4 | — | 8 | 2 | no | — |
| 315 | D4 | — | 424 | 4 | no | — |
| 316 | D4 | — | 424 | 4 | no | — |
| 317 | D4 | — | 424 | 8 | no | — |
| 318 | D4 | — | 424 | 4 | no | — |
| 319 | D4 | — | 424 | 2 | no | — |
| 320 | D4 | — | 212 | 8 | no | — |
| 321 | D4 | — | 212 | 4 | no | — |
| 322 | D4 | — | 212 | 4 | no | — |
| 323 | D4 | — | 212 | 4 | no | — |
| 324 | D4 | — | 212 | 4 | no | — |
| 325 | C2×C4 | — | 2 | 4 | no | — |
| 326 | C2×C4 | — | 2 | 2 | no | — |
| 327 | C2×C4 | — | 2 | 2 | no | — |
| 328 | C2×C4 | — | 4 | 4 | no | — |
| 329 | C2×C4 | — | 106 | 4 | no | — |
| 330 | C2×C4 | — | 212 | 8 | no | — |
| 331 | C2×C4 | #13133187 | 1 | 2 | yes | — |
| 332 | C2×C4 | #13133187 | 1 | 1 | yes | characteristic |
| 333 | C2×C4 | C2×D4×D53 | 1 | 2 | yes | — |
| 334 | C2×C4 | C22×D212 | 1 | 1 | yes | characteristic |
| 335 | C8 | — | 2 | 8 | no | — |
| 336 | C8 | — | 106 | 4 | no | — |
| 337 | C22 | — | 2 | 2 | no | — |
| 338 | C22 | — | 2 | 1 | no | — |
| 339 | C22 | — | 4 | 4 | no | — |
| 340 | C22 | — | 4 | 2 | no | — |
| 341 | C22 | — | 848 | 4 | no | — |
| 342 | C22 | — | 848 | 8 | no | — |
| 343 | C22 | — | 424 | 4 | no | — |
| 344 | C22 | — | 424 | 2 | no | — |
| 345 | C22 | — | 212 | 4 | no | — |
| 346 | C22 | — | 212 | 4 | no | — |
| 347 | C22 | — | 212 | 4 | no | — |
| 348 | C22 | C2×#13133187 | 1 | 1 | yes | characteristic |
| 349 | C4 | — | 2 | 2 | no | — |
| 350 | C4 | — | 2 | 1 | no | — |
| 351 | C4 | — | 4 | 2 | no | — |
| 352 | C4 | — | 212 | 4 | no | — |
| 353 | C4 | #16810792 | 1 | 4 | yes | — |
| 354 | C4 | #16810793 | 1 | 2 | yes | — |
| 355 | C2 | — | 4 | 1 | no | — |
| 356 | C2 | — | 8 | 2 | no | — |
| 357 | C2 | — | 848 | 2 | no | — |
| 358 | C2 | — | 424 | 4 | no | — |
| 359 | C2 | C2×#16810792 | 1 | 2 | yes | — |
| 360 | C2 | C2×#16810793 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20289120 | C2 | semidirect |
| 2. #20285168 | C2 | semidirect |
| 3. #20285167 | C2 | semidirect |
| 4. #20274005 | C2 | semidirect |
| 5. #20273306 | C2 | semidirect |
| 6. C53×#1525 | C2 | semidirect |
| 9. #16811365 | C22 | semidirect |
| 17. C2×#13133214 | C22 | semidirect |
| 18. #16811013 | C22 | semidirect |
| 19. #16811012 | C22 | semidirect |
| 24. C4×#11719917 | C22 | semidirect |
| 25. #16810362 | C22 | semidirect |
| 27. C4×M16×C53 | C22 | semidirect |
| 28. C53×#329 | C22 | semidirect |
| 180. #1525 | D53 | semidirect |
| 206. C4×M16 | C2×D53 | semidirect |
| 208. #329 | C2×D53 | semidirect |
| 209. C53 | #19073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289120 | 2 |
| #20285168 | 2 |
| #20285167 | 2 |
| #20274005 | 2 |
| #20273306 | 2 |
| C53×#1525 | 2 |
| #19073 | 53 |