Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
378 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 47 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 | #20276735 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20276727 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20274024 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20272875 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20272866 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20272863 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C53×#3289 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #16811373 | C22 | 1 | 1 | yes | characteristic |
| 9 | #16811029 | — | 2 | 1 | no | — |
| 10 | #16810813 | — | 2 | 1 | no | — |
| 11 | #16810806 | — | 2 | 1 | no | — |
| 12 | #16810421 | — | 2 | 1 | no | — |
| 13 | #16810420 | C22 | 1 | 1 | yes | characteristic |
| 14 | #16810418 | C22 | 1 | 1 | yes | characteristic |
| 15 | #16810414 | — | 2 | 1 | no | — |
| 16 | #16810364 | — | 2 | 1 | no | — |
| 17 | #16810363 | C22 | 1 | 1 | yes | characteristic |
| 18 | C53×#578 | — | 2 | 1 | no | — |
| 19 | C53×#577 | — | 2 | 1 | no | — |
| 20 | C53×#497 | C22 | 1 | 1 | yes | characteristic |
| 21 | C53×#473 | — | 2 | 1 | no | — |
| 22 | C53×#471 | — | 2 | 1 | no | — |
| 23 | C53×#456 | — | 2 | 1 | no | — |
| 24 | C53×#455 | C22 | 1 | 1 | yes | characteristic |
| 25 | C53×#454 | C22 | 1 | 1 | yes | characteristic |
| 26 | C53×#444 | — | 2 | 1 | no | — |
| 27 | #13133247 | — | 4 | 1 | no | — |
| 28 | #13133215 | — | 2 | 1 | no | — |
| 29 | #13133210 | — | 4 | 1 | no | — |
| 30 | #13133209 | — | 2 | 1 | no | — |
| 31 | #13133198 | — | 2 | 1 | no | — |
| 32 | #13133198 | — | 4 | 1 | no | — |
| 33 | #13133194 | — | 4 | 1 | no | — |
| 34 | #13133150 | — | 4 | 1 | no | — |
| 35 | #13133148 | — | 4 | 1 | no | — |
| 36 | #13133144 | — | 4 | 1 | no | — |
| 37 | #13133136 | — | 2 | 1 | no | — |
| 38 | #13133132 | — | 2 | 1 | no | — |
| 39 | #13133132 | — | 4 | 1 | no | — |
| 40 | #13133128 | — | 2 | 1 | no | — |
| 41 | 2−1+4×C53 | — | 2 | 1 | no | — |
| 42 | 2−1+4×C53 | D4 | 1 | 1 | yes | characteristic |
| 43 | H(5,𝔽2)×C53 | D4 | 1 | 1 | yes | characteristic |
| 44 | #137×C53 | — | 2 | 1 | no | — |
| 45 | #137×C53 | — | 2 | 1 | no | — |
| 46 | #137×C53 | — | 2 | 1 | no | — |
| 47 | #137×C53 | — | 4 | 1 | no | — |
| 48 | #137×C53 | — | 4 | 1 | no | — |
| 49 | #137×C53 | — | 4 | 1 | no | — |
| 50 | AGL(1,ℤ/8)×C53 | — | 2 | 1 | no | — |
| 51 | AGL(1,ℤ/8)×C53 | — | 4 | 1 | no | — |
| 52 | #135×C53 | — | 2 | 1 | no | — |
| 53 | #135×C53 | — | 4 | 1 | no | — |
| 54 | #135×C53 | — | 4 | 1 | no | — |
| 55 | C2×Q16×C53 | — | 2 | 1 | no | — |
| 56 | C2×Q16×C53 | — | 4 | 1 | no | — |
| 57 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 58 | C2×SD16×C53 | — | 4 | 1 | no | — |
| 59 | #131×C53 | — | 2 | 1 | no | — |
| 60 | #131×C53 | — | 2 | 1 | no | — |
| 61 | C4⋊Q8×C53 | D4 | 1 | 1 | yes | characteristic |
| 62 | #124×C53 | C23 | 1 | 1 | yes | characteristic |
| 63 | #108×C53 | — | 2 | 1 | no | — |
| 64 | #104×C53 | — | 2 | 1 | no | — |
| 65 | #104×C53 | — | 2 | 1 | no | — |
| 66 | #101×C53 | — | 2 | 1 | no | — |
| 67 | #101×C53 | D4 | 1 | 1 | yes | characteristic |
| 68 | #100×C53 | D4 | 1 | 1 | yes | characteristic |
| 69 | #97×C53 | D4 | 1 | 1 | yes | characteristic |
| 70 | #41×C53 | — | 2 | 1 | no | — |
| 71 | #41×C53 | — | 2 | 1 | no | — |
| 72 | #41×C53 | — | 4 | 1 | no | — |
| 73 | #41×C53 | — | 4 | 1 | no | — |
| 74 | #41×C53 | — | 4 | 1 | no | — |
| 75 | #41×C53 | — | 4 | 1 | no | — |
| 76 | #41×C53 | — | 4 | 1 | no | — |
| 77 | #41×C53 | — | 8 | 1 | no | — |
| 78 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 79 | C2×Q8×C53 | — | 4 | 1 | no | — |
| 80 | C2×Q8×C53 | — | 4 | 1 | no | — |
| 81 | C2×Q8×C53 | — | 4 | 1 | no | — |
| 82 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 83 | C2×D4×C53 | — | 4 | 1 | no | — |
| 84 | C2×D4×C53 | — | 4 | 1 | no | — |
| 85 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 86 | C22×Dic53 | — | 2 | 1 | no | — |
| 87 | C2×Dic106 | — | 2 | 1 | no | — |
| 88 | Q16×C53 | — | 2 | 1 | no | — |
| 89 | Q16×C53 | — | 4 | 1 | no | — |
| 90 | Q16×C53 | — | 4 | 1 | no | — |
| 91 | Q16×C53 | — | 4 | 1 | no | — |
| 92 | Q16×C53 | — | 4 | 1 | no | — |
| 93 | Q16×C53 | — | 4 | 1 | no | — |
| 94 | SD16×C53 | — | 2 | 1 | no | — |
| 95 | SD16×C53 | — | 2 | 1 | no | — |
| 96 | SD16×C53 | — | 4 | 1 | no | — |
| 97 | SD16×C53 | — | 4 | 1 | no | — |
| 98 | SD16×C53 | — | 4 | 1 | no | — |
| 99 | SD16×C53 | — | 4 | 1 | no | — |
| 100 | SD16×C53 | — | 4 | 1 | no | — |
| 101 | SD16×C53 | — | 4 | 1 | no | — |
| 102 | D8×C53 | — | 2 | 1 | no | — |
| 103 | D8×C53 | — | 4 | 1 | no | — |
| 104 | M16×C53 | — | 2 | 1 | no | — |
| 105 | M16×C53 | — | 2 | 1 | no | — |
| 106 | M16×C53 | — | 4 | 1 | no | — |
| 107 | M16×C53 | — | 4 | 1 | no | — |
| 108 | C2×C8×C53 | — | 2 | 1 | no | — |
| 109 | C2×C8×C53 | — | 4 | 1 | no | — |
| 110 | C2×C8×C53 | — | 4 | 1 | no | — |
| 111 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 112 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 113 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 115 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 116 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 117 | C22⋊Dic53 | — | 8 | 1 | no | — |
| 118 | #11719925 | — | 8 | 1 | no | — |
| 119 | #11719923 | — | 8 | 1 | no | — |
| 120 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 121 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 122 | #11719919 | — | 4 | 1 | no | — |
| 123 | #11719919 | — | 4 | 1 | no | — |
| 124 | #11719919 | — | 4 | 1 | no | — |
| 125 | #11719919 | — | 8 | 1 | no | — |
| 126 | C4×Dic53 | — | 2 | 1 | no | — |
| 127 | #11719917 | — | 4 | 1 | no | — |
| 128 | C2×#88322 | — | 4 | 1 | no | — |
| 129 | C23×C53 | — | 2 | 1 | no | — |
| 130 | C23×C53 | — | 4 | 1 | no | — |
| 131 | Q8×C53 | — | 2 | 1 | no | — |
| 132 | Q8×C53 | — | 2 | 1 | no | — |
| 133 | Q8×C53 | — | 4 | 1 | no | — |
| 134 | Q8×C53 | — | 4 | 1 | no | — |
| 135 | Q8×C53 | — | 4 | 1 | no | — |
| 136 | Q8×C53 | — | 4 | 1 | no | — |
| 137 | Q8×C53 | — | 8 | 1 | no | — |
| 138 | D4×C53 | — | 2 | 1 | no | — |
| 139 | D4×C53 | — | 2 | 1 | no | — |
| 140 | D4×C53 | — | 4 | 1 | no | — |
| 141 | D4×C53 | — | 4 | 1 | no | — |
| 142 | D4×C53 | — | 4 | 1 | no | — |
| 143 | D4×C53 | — | 4 | 1 | no | — |
| 144 | D4×C53 | — | 8 | 1 | no | — |
| 145 | D4×C53 | — | 8 | 1 | no | — |
| 146 | C2×C4×C53 | — | 2 | 1 | no | — |
| 147 | C2×C4×C53 | — | 2 | 1 | no | — |
| 148 | C2×C4×C53 | — | 4 | 1 | no | — |
| 149 | C2×C4×C53 | — | 4 | 1 | no | — |
| 150 | C2×C4×C53 | — | 4 | 1 | no | — |
| 151 | C2×C4×C53 | — | 4 | 1 | no | — |
| 152 | C2×C4×C53 | — | 8 | 1 | no | — |
| 153 | C2×C4×C53 | — | 8 | 1 | no | — |
| 154 | C2×C4×C53 | — | 8 | 1 | no | — |
| 155 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 156 | C2×Dic53 | — | 4 | 1 | no | — |
| 157 | C2×Dic53 | — | 4 | 1 | no | — |
| 158 | C2×Dic53 | — | 8 | 1 | no | — |
| 159 | C2×Dic53 | — | 8 | 1 | no | — |
| 160 | Dic106 | — | 8 | 1 | no | — |
| 161 | C8×C53 | — | 2 | 1 | no | — |
| 162 | C8×C53 | — | 2 | 1 | no | — |
| 163 | C8×C53 | — | 4 | 1 | no | — |
| 164 | C8×C53 | — | 4 | 1 | no | — |
| 165 | #88322 | — | 4 | 2 | no | — |
| 166 | #88322 | — | 8 | 1 | no | — |
| 167 | #13680 | — | 53 | 1 | no | maximal, Sylow |
| 168 | C22×C53 | — | 4 | 1 | no | — |
| 169 | C22×C53 | — | 4 | 1 | no | — |
| 170 | C22×C53 | — | 4 | 1 | no | — |
| 171 | C22×C53 | — | 8 | 1 | no | — |
| 172 | C22×C53 | — | 16 | 1 | no | — |
| 173 | C22×C53 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 174 | C4×C53 | — | 2 | 1 | no | — |
| 175 | C4×C53 | — | 4 | 1 | no | — |
| 176 | C4×C53 | — | 4 | 1 | no | — |
| 177 | C4×C53 | — | 4 | 1 | no | — |
| 178 | C4×C53 | — | 4 | 1 | no | — |
| 179 | C4×C53 | — | 8 | 1 | no | — |
| 180 | Dic53 | — | 8 | 1 | no | — |
| 181 | Dic53 | — | 8 | 1 | no | — |
| 182 | Dic53 | — | 16 | 1 | no | — |
| 183 | #3289 | D53 | 1 | 1 | yes | characteristic |
| 184 | #2203 | — | 53 | 1 | no | — |
| 185 | #2201 | — | 53 | 1 | no | — |
| 186 | #1660 | — | 53 | 1 | no | — |
| 187 | #1407 | — | 53 | 1 | no | — |
| 188 | #1404 | — | 53 | 1 | no | — |
| 189 | #1403 | — | 53 | 1 | no | — |
| 190 | C2×C53 | — | 2 | 1 | no | — |
| 191 | C2×C53 | — | 8 | 1 | no | — |
| 192 | C2×C53 | — | 8 | 1 | no | — |
| 193 | C2×C53 | — | 8 | 1 | no | — |
| 194 | C2×C53 | #2196 | 1 | 1 | yes | characteristic |
| 195 | #578 | — | 2 | 1 | no | — |
| 196 | #577 | — | 2 | 1 | no | — |
| 197 | #563 | — | 53 | 1 | no | — |
| 198 | #501 | — | 106 | 1 | no | — |
| 199 | #497 | C2×D53 | 1 | 1 | yes | characteristic |
| 200 | #473 | — | 2 | 1 | no | — |
| 201 | #471 | — | 2 | 1 | no | — |
| 202 | #458 | — | 106 | 1 | no | — |
| 203 | #456 | — | 2 | 1 | no | — |
| 204 | #456 | — | 106 | 1 | no | — |
| 205 | #455 | C2×D53 | 1 | 1 | yes | characteristic |
| 206 | #454 | C2×D53 | 1 | 1 | yes | characteristic |
| 207 | #444 | — | 2 | 1 | no | — |
| 208 | #356 | — | 106 | 1 | no | — |
| 209 | #355 | — | 53 | 1 | no | — |
| 210 | #354 | — | 53 | 1 | no | — |
| 211 | #352 | — | 106 | 1 | no | — |
| 212 | #330 | — | 106 | 1 | no | — |
| 213 | #329 | — | 53 | 1 | no | — |
| 214 | C53 | #13680 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 215 | 2−1+4 | — | 2 | 1 | no | — |
| 216 | 2−1+4 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 217 | H(5,𝔽2) | C22⋊D53 | 1 | 1 | yes | characteristic |
| 218 | #137 | — | 2 | 1 | no | — |
| 219 | #137 | — | 2 | 1 | no | — |
| 220 | #137 | — | 2 | 1 | no | — |
| 221 | #137 | — | 4 | 1 | no | — |
| 222 | #137 | — | 4 | 1 | no | — |
| 223 | #137 | — | 4 | 1 | no | — |
| 224 | #137 | — | 212 | 1 | no | — |
| 225 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 226 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 227 | #135 | — | 2 | 1 | no | — |
| 228 | #135 | — | 4 | 1 | no | — |
| 229 | #135 | — | 4 | 1 | no | — |
| 230 | C2×Q16 | — | 2 | 1 | no | — |
| 231 | C2×Q16 | — | 4 | 1 | no | — |
| 232 | C2×SD16 | — | 2 | 1 | no | — |
| 233 | C2×SD16 | — | 4 | 1 | no | — |
| 234 | #131 | — | 2 | 1 | no | — |
| 235 | #131 | — | 2 | 1 | no | — |
| 236 | C4⋊Q8 | — | 106 | 1 | no | — |
| 237 | C4⋊Q8 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 238 | #126 | — | 212 | 1 | no | — |
| 239 | #125 | — | 106 | 1 | no | — |
| 240 | #124 | C22×D53 | 1 | 1 | yes | characteristic |
| 241 | #123 | — | 106 | 1 | no | — |
| 242 | #123 | — | 212 | 1 | no | — |
| 243 | C22⋊Q8 | — | 212 | 1 | no | — |
| 244 | #108 | — | 2 | 1 | no | — |
| 245 | #107 | — | 212 | 1 | no | — |
| 246 | #106 | — | 212 | 1 | no | — |
| 247 | #104 | — | 2 | 1 | no | — |
| 248 | #104 | — | 2 | 1 | no | — |
| 249 | #104 | — | 212 | 1 | no | — |
| 250 | #101 | — | 2 | 1 | no | — |
| 251 | #101 | — | 106 | 1 | no | — |
| 252 | #101 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 253 | #100 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 254 | #99 | — | 106 | 1 | no | — |
| 255 | #99 | — | 212 | 1 | no | — |
| 256 | #97 | — | 106 | 1 | no | — |
| 257 | #97 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 258 | #41 | — | 2 | 1 | no | — |
| 259 | #41 | — | 2 | 1 | no | — |
| 260 | #41 | — | 4 | 1 | no | — |
| 261 | #41 | — | 4 | 1 | no | — |
| 262 | #41 | — | 4 | 1 | no | — |
| 263 | #41 | — | 4 | 1 | no | — |
| 264 | #41 | — | 4 | 1 | no | — |
| 265 | #41 | — | 8 | 1 | no | — |
| 266 | C2×Q8 | — | 2 | 1 | no | — |
| 267 | C2×Q8 | — | 4 | 1 | no | — |
| 268 | C2×Q8 | — | 4 | 1 | no | — |
| 269 | C2×Q8 | — | 4 | 1 | no | — |
| 270 | C2×Q8 | — | 106 | 1 | no | — |
| 271 | C2×Q8 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 272 | C2×D4 | — | 4 | 1 | no | — |
| 273 | C2×D4 | — | 4 | 1 | no | — |
| 274 | C2×D4 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 275 | C22×C4 | — | 106 | 1 | no | — |
| 276 | Q16 | — | 2 | 1 | no | — |
| 277 | Q16 | — | 4 | 1 | no | — |
| 278 | Q16 | — | 4 | 1 | no | — |
| 279 | Q16 | — | 4 | 1 | no | — |
| 280 | Q16 | — | 4 | 1 | no | — |
| 281 | Q16 | — | 4 | 1 | no | — |
| 282 | Q16 | — | 424 | 1 | no | — |
| 283 | SD16 | — | 2 | 1 | no | — |
| 284 | SD16 | — | 2 | 1 | no | — |
| 285 | SD16 | — | 4 | 1 | no | — |
| 286 | SD16 | — | 4 | 1 | no | — |
| 287 | SD16 | — | 4 | 1 | no | — |
| 288 | SD16 | — | 4 | 1 | no | — |
| 289 | SD16 | — | 4 | 1 | no | — |
| 290 | SD16 | — | 4 | 1 | no | — |
| 291 | SD16 | — | 424 | 1 | no | — |
| 292 | D8 | — | 2 | 1 | no | — |
| 293 | D8 | — | 4 | 1 | no | — |
| 294 | M16 | — | 2 | 1 | no | — |
| 295 | M16 | — | 2 | 1 | no | — |
| 296 | M16 | — | 4 | 1 | no | — |
| 297 | M16 | — | 4 | 1 | no | — |
| 298 | M16 | — | 212 | 1 | no | — |
| 299 | C2×C8 | — | 2 | 1 | no | — |
| 300 | C2×C8 | — | 4 | 1 | no | — |
| 301 | C2×C8 | — | 4 | 1 | no | — |
| 302 | C2×C8 | — | 212 | 1 | no | — |
| 303 | C4⋊C4 | — | 4 | 1 | no | — |
| 304 | C4⋊C4 | — | 106 | 1 | no | — |
| 305 | C4⋊C4 | — | 106 | 1 | no | — |
| 306 | C4⋊C4 | — | 424 | 1 | no | — |
| 307 | C4⋊C4 | — | 212 | 1 | no | — |
| 308 | C4⋊C4 | — | 212 | 1 | no | — |
| 309 | C4⋊C4 | — | 212 | 1 | no | — |
| 310 | C22⋊C4 | — | 4 | 1 | no | — |
| 311 | C22⋊C4 | — | 106 | 1 | no | — |
| 312 | C22⋊C4 | — | 424 | 1 | no | — |
| 313 | C22⋊C4 | — | 212 | 1 | no | — |
| 314 | C22⋊C4 | — | 212 | 1 | no | — |
| 315 | C42 | — | 106 | 1 | no | — |
| 316 | C42 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 317 | C23 | — | 2 | 1 | no | — |
| 318 | C23 | — | 4 | 1 | no | — |
| 319 | Q8 | — | 2 | 1 | no | — |
| 320 | Q8 | — | 2 | 1 | no | — |
| 321 | Q8 | — | 4 | 1 | no | — |
| 322 | Q8 | — | 4 | 1 | no | — |
| 323 | Q8 | — | 4 | 1 | no | — |
| 324 | Q8 | — | 4 | 1 | no | — |
| 325 | Q8 | — | 8 | 1 | no | — |
| 326 | Q8 | — | 424 | 1 | no | — |
| 327 | D4 | — | 2 | 1 | no | — |
| 328 | D4 | — | 2 | 1 | no | — |
| 329 | D4 | — | 4 | 1 | no | — |
| 330 | D4 | — | 4 | 1 | no | — |
| 331 | D4 | — | 4 | 1 | no | — |
| 332 | D4 | — | 4 | 1 | no | — |
| 333 | D4 | — | 8 | 1 | no | — |
| 334 | D4 | — | 8 | 1 | no | — |
| 335 | C2×C4 | — | 2 | 1 | no | — |
| 336 | C2×C4 | — | 2 | 1 | no | — |
| 337 | C2×C4 | — | 4 | 1 | no | — |
| 338 | C2×C4 | — | 4 | 1 | no | — |
| 339 | C2×C4 | — | 4 | 1 | no | — |
| 340 | C2×C4 | — | 4 | 1 | no | — |
| 341 | C2×C4 | — | 8 | 1 | no | — |
| 342 | C2×C4 | — | 8 | 1 | no | — |
| 343 | C2×C4 | — | 8 | 1 | no | — |
| 344 | C2×C4 | — | 424 | 1 | no | — |
| 345 | C2×C4 | — | 424 | 1 | no | — |
| 346 | C2×C4 | — | 212 | 1 | no | — |
| 347 | C2×C4 | — | 212 | 1 | no | — |
| 348 | C2×C4 | #13133186 | 1 | 1 | yes | characteristic |
| 349 | C8 | — | 2 | 1 | no | — |
| 350 | C8 | — | 2 | 1 | no | — |
| 351 | C8 | — | 4 | 1 | no | — |
| 352 | C8 | — | 4 | 1 | no | — |
| 353 | C8 | — | 424 | 1 | no | — |
| 354 | C8 | — | 212 | 2 | no | — |
| 355 | C22 | — | 4 | 1 | no | — |
| 356 | C22 | — | 4 | 1 | no | — |
| 357 | C22 | — | 4 | 1 | no | — |
| 358 | C22 | — | 8 | 1 | no | — |
| 359 | C22 | — | 16 | 1 | no | — |
| 360 | C22 | #16810810 | 1 | 1 | yes | characteristic |
| 361 | C4 | — | 2 | 1 | no | — |
| 362 | C4 | — | 4 | 1 | no | — |
| 363 | C4 | — | 4 | 1 | no | — |
| 364 | C4 | — | 4 | 1 | no | — |
| 365 | C4 | — | 4 | 1 | no | — |
| 366 | C4 | — | 8 | 1 | no | — |
| 367 | C4 | — | 848 | 1 | no | — |
| 368 | C4 | — | 424 | 1 | no | — |
| 369 | C4 | — | 424 | 1 | no | — |
| 370 | C2 | — | 2 | 1 | no | — |
| 371 | C2 | — | 8 | 1 | no | — |
| 372 | C2 | — | 8 | 1 | no | — |
| 373 | C2 | — | 8 | 1 | no | — |
| 374 | C2 | #20276699 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20276735 | C2 | semidirect |
| 2. #20276727 | C2 | semidirect |
| 3. #20274024 | C2 | semidirect |
| 4. #20272875 | C2 | semidirect |
| 5. #20272866 | C2 | semidirect |
| 6. #20272863 | C2 | semidirect |
| 214. C53 | #13680 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276735 | 2 |
| #20276727 | 2 |
| #20274024 | 2 |
| #20272875 | 2 |
| #20272866 | 2 |
| #20272863 | 2 |
| C53×#3289 | 2 |
| #13680 | 53 |