Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
346 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 41 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 | A4×C22⋊D7 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×C7⋊SL(2,ℤ/4) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C7×GL(2,ℤ/4) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10621482 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | D7×SL(2,ℤ/4) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | S4×Dic7 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10621477 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #90282 | — | 3 | 1 | no | maximal, Hall |
| 9 | C22×C7×A4 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×A4×D7 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C7×S4 | C22 | 1 | 1 | yes | characteristic |
| 12 | #66684 | — | 4 | 1 | no | maximal |
| 13 | A4×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 14 | C7⋊SL(2,ℤ/4) | C22 | 1 | 1 | yes | characteristic |
| 15 | C7⋊SL(2,ℤ/4) | C22 | 1 | 1 | yes | characteristic |
| 16 | C7×SL(2,ℤ/4) | C22 | 1 | 1 | yes | characteristic |
| 17 | C22×C22⋊D7 | D3 | 1 | 1 | yes | characteristic, complemented |
| 18 | C2×#1159 | — | 3 | 1 | no | — |
| 19 | C7×#120 | — | 3 | 1 | no | — |
| 20 | C2×C22⋊Dic7 | — | 3 | 1 | no | — |
| 21 | #6502 | — | 3 | 1 | no | — |
| 22 | #6502 | — | 3 | 1 | no | — |
| 23 | #6501 | — | 3 | 1 | no | — |
| 24 | #6500 | — | 3 | 1 | no | — |
| 25 | D4×Dic7 | — | 3 | 1 | no | — |
| 26 | #6449 | — | 3 | 1 | no | — |
| 27 | #6448 | — | 3 | 1 | no | — |
| 28 | #6446 | — | 3 | 1 | no | — |
| 29 | (C22⋊D7)⋊C4 | — | 3 | 1 | no | — |
| 30 | D7×C22⋊C4 | — | 3 | 1 | no | — |
| 31 | #6441 | — | 3 | 1 | no | — |
| 32 | #5914 | — | 7 | 1 | no | maximal, Hall |
| 33 | C2×C7×A4 | — | 2 | 1 | no | — |
| 34 | C2×C7×A4 | C23 | 1 | 1 | yes | characteristic |
| 35 | A4×D7 | — | 2 | 1 | no | — |
| 36 | C7×S4 | — | 2 | 1 | no | — |
| 37 | C2×Dic21 | — | 4 | 1 | no | — |
| 38 | C7×#67 | — | 4 | 1 | no | — |
| 39 | C3×C22⋊D7 | — | 4 | 1 | no | — |
| 40 | #4248 | — | 4 | 1 | no | — |
| 41 | #4245 | — | 4 | 1 | no | — |
| 42 | D3×Dic7 | — | 4 | 1 | no | — |
| 43 | Dic3×D7 | — | 4 | 1 | no | — |
| 44 | C24×C7 | C2×D3 | 1 | 1 | yes | characteristic |
| 45 | C23×D7 | C2×D3 | 1 | 1 | yes | characteristic |
| 46 | C2×C7×D4 | — | 3 | 1 | no | — |
| 47 | C2×C7×D4 | — | 3 | 1 | no | — |
| 48 | C2×C7×D4 | — | 3 | 1 | no | — |
| 49 | C2×C22⋊D7 | — | 3 | 1 | no | — |
| 50 | C2×C22⋊D7 | — | 3 | 1 | no | — |
| 51 | C2×C22⋊D7 | — | 3 | 1 | no | — |
| 52 | C2×C22⋊D7 | — | 3 | 1 | no | — |
| 53 | C2×C22⋊D7 | — | 3 | 1 | no | — |
| 54 | C2×C22⋊D7 | — | 3 | 1 | no | — |
| 55 | C22×Dic7 | — | 3 | 1 | no | — |
| 56 | C22×Dic7 | — | 3 | 1 | no | — |
| 57 | C22×Dic7 | — | 3 | 1 | no | — |
| 58 | C22×Dic7 | C2×D3 | 1 | 1 | yes | characteristic |
| 59 | #1159 | — | 6 | 1 | no | — |
| 60 | #1159 | — | 6 | 1 | no | — |
| 61 | #1159 | — | 6 | 1 | no | — |
| 62 | #1159 | — | 6 | 1 | no | — |
| 63 | C2×C4×D7 | — | 3 | 1 | no | — |
| 64 | C2×C4×D7 | — | 3 | 1 | no | — |
| 65 | C2×Dic14 | — | 3 | 1 | no | — |
| 66 | C7×C22⋊C4 | — | 3 | 1 | no | — |
| 67 | C7×C22⋊C4 | — | 3 | 1 | no | — |
| 68 | C7×C22⋊C4 | — | 3 | 1 | no | — |
| 69 | C22⋊Dic7 | — | 3 | 1 | no | — |
| 70 | C22⋊Dic7 | — | 3 | 1 | no | — |
| 71 | C22⋊Dic7 | — | 3 | 1 | no | — |
| 72 | C22⋊Dic7 | — | 3 | 1 | no | — |
| 73 | C22⋊Dic7 | — | 3 | 1 | no | — |
| 74 | (C2×D7)⋊C4 | — | 3 | 1 | no | — |
| 75 | (C2×D7)⋊C4 | — | 3 | 1 | no | — |
| 76 | (C2×D7)⋊C4 | — | 3 | 1 | no | — |
| 77 | (C2×D7)⋊C4 | — | 3 | 1 | no | — |
| 78 | C4⋊Dic7 | — | 3 | 1 | no | — |
| 79 | C4⋊Dic7 | — | 3 | 1 | no | — |
| 80 | Dic7⋊C4 | — | 3 | 1 | no | — |
| 81 | Dic7⋊C4 | — | 3 | 1 | no | — |
| 82 | C4×Dic7 | — | 3 | 1 | no | — |
| 83 | D4×A4 | — | 7 | 1 | no | — |
| 84 | GL(2,ℤ/4) | — | 7 | 1 | no | — |
| 85 | GL(2,ℤ/4) | D7 | 1 | 1 | yes | characteristic, complemented |
| 86 | C2×SL(2,ℤ/4) | — | 7 | 1 | no | — |
| 87 | C2×SL(2,ℤ/4) | — | 7 | 1 | no | — |
| 88 | C4×S4 | — | 7 | 1 | no | — |
| 89 | A4⋊Q8 | — | 7 | 1 | no | — |
| 90 | C22×C3×C7 | — | 4 | 1 | no | — |
| 91 | C2×D3×C7 | — | 4 | 1 | no | — |
| 92 | C2×C3×D7 | — | 4 | 1 | no | — |
| 93 | C7×A4 | #41 | 1 | 1 | yes | characteristic, complemented |
| 94 | Dic21 | — | 4 | 1 | no | — |
| 95 | Dic21 | — | 4 | 1 | no | — |
| 96 | C3×Dic7 | — | 4 | 1 | no | — |
| 97 | C7×Dic3 | — | 4 | 1 | no | — |
| 98 | #546 | — | 21 | 1 | no | Sylow |
| 99 | C23×C7 | — | 2 | 1 | no | — |
| 100 | C23×C7 | — | 3 | 1 | no | — |
| 101 | C23×C7 | — | 3 | 1 | no | — |
| 102 | C23×C7 | — | 3 | 1 | no | — |
| 103 | C23×C7 | — | 6 | 1 | no | — |
| 104 | C23×C7 | C22×D3 | 1 | 1 | yes | characteristic |
| 105 | C22×D7 | — | 2 | 1 | no | — |
| 106 | C22×D7 | — | 3 | 1 | no | — |
| 107 | C22×D7 | — | 3 | 1 | no | — |
| 108 | C22×D7 | — | 6 | 1 | no | — |
| 109 | C7×D4 | — | 6 | 1 | no | — |
| 110 | C7×D4 | — | 6 | 1 | no | — |
| 111 | C7×D4 | — | 6 | 1 | no | — |
| 112 | C7×D4 | — | 6 | 1 | no | — |
| 113 | C7×D4 | — | 12 | 1 | no | — |
| 114 | C2×C4×C7 | — | 3 | 1 | no | — |
| 115 | C2×C4×C7 | — | 3 | 1 | no | — |
| 116 | C2×C4×C7 | — | 3 | 1 | no | — |
| 117 | C22⋊D7 | — | 3 | 1 | no | — |
| 118 | C22⋊D7 | — | 3 | 1 | no | — |
| 119 | C22⋊D7 | — | 3 | 1 | no | — |
| 120 | C22⋊D7 | — | 6 | 1 | no | — |
| 121 | C22⋊D7 | — | 6 | 1 | no | — |
| 122 | C22⋊D7 | — | 6 | 1 | no | — |
| 123 | C22⋊D7 | — | 12 | 1 | no | — |
| 124 | C22⋊D7 | S4 | 1 | 1 | yes | characteristic, complemented |
| 125 | C2×Dic7 | — | 3 | 1 | no | — |
| 126 | C2×Dic7 | — | 3 | 1 | no | — |
| 127 | C2×Dic7 | — | 3 | 1 | no | — |
| 128 | C2×Dic7 | — | 3 | 1 | no | — |
| 129 | C2×Dic7 | — | 3 | 1 | no | — |
| 130 | C2×Dic7 | — | 3 | 1 | no | — |
| 131 | C2×Dic7 | — | 6 | 1 | no | — |
| 132 | C2×Dic7 | — | 6 | 1 | no | — |
| 133 | C2×Dic7 | — | 6 | 1 | no | — |
| 134 | C2×Dic7 | — | 6 | 1 | no | — |
| 135 | C2×Dic7 | — | 12 | 1 | no | — |
| 136 | C4×D7 | — | 6 | 1 | no | — |
| 137 | C4×D7 | — | 6 | 1 | no | — |
| 138 | C4×D7 | — | 12 | 1 | no | — |
| 139 | Dic14 | — | 6 | 1 | no | — |
| 140 | Dic14 | — | 6 | 1 | no | — |
| 141 | C22×A4 | — | 7 | 1 | no | — |
| 142 | C22×A4 | C2×D7 | 1 | 1 | yes | characteristic |
| 143 | C2×S4 | C2×D7 | 1 | 1 | yes | characteristic |
| 144 | #237 | — | 28 | 1 | no | — |
| 145 | C4×A4 | — | 7 | 1 | no | — |
| 146 | SL(2,ℤ/4) | — | 7 | 1 | no | — |
| 147 | SL(2,ℤ/4) | — | 7 | 1 | no | — |
| 148 | SL(2,ℤ/4) | C2×D7 | 1 | 1 | yes | characteristic |
| 149 | C2×C3×C7 | — | 4 | 1 | no | — |
| 150 | C2×C3×C7 | — | 8 | 1 | no | — |
| 151 | C3×D7 | — | 8 | 1 | no | — |
| 152 | D3×C7 | — | 8 | 1 | no | — |
| 153 | C2×#41 | — | 21 | 1 | no | — |
| 154 | C22×D4 | — | 7 | 1 | no | — |
| 155 | #124 | — | 21 | 1 | no | — |
| 156 | #123 | — | 21 | 1 | no | — |
| 157 | #123 | — | 21 | 1 | no | — |
| 158 | C22⋊Q8 | — | 21 | 1 | no | — |
| 159 | #121 | — | 21 | 1 | no | — |
| 160 | #121 | — | 21 | 1 | no | — |
| 161 | #121 | — | 21 | 1 | no | — |
| 162 | #120 | — | 3 | 1 | no | — |
| 163 | #120 | — | 21 | 1 | no | — |
| 164 | C4×D4 | — | 21 | 1 | no | — |
| 165 | C4×D4 | — | 21 | 1 | no | — |
| 166 | C2×C22⋊C4 | — | 21 | 1 | no | — |
| 167 | C2×C22⋊C4 | — | 21 | 1 | no | — |
| 168 | C22×C7 | — | 3 | 1 | no | — |
| 169 | C22×C7 | — | 3 | 1 | no | — |
| 170 | C22×C7 | — | 3 | 1 | no | — |
| 171 | C22×C7 | — | 6 | 1 | no | — |
| 172 | C22×C7 | — | 6 | 1 | no | — |
| 173 | C22×C7 | — | 6 | 1 | no | — |
| 174 | C22×C7 | — | 6 | 1 | no | — |
| 175 | C22×C7 | — | 6 | 1 | no | — |
| 176 | C22×C7 | — | 6 | 1 | no | — |
| 177 | C22×C7 | — | 6 | 1 | no | — |
| 178 | C22×C7 | #237 | 1 | 1 | yes | characteristic, complemented |
| 179 | C22×C7 | C2×S4 | 1 | 1 | yes | characteristic |
| 180 | C2×D7 | — | 3 | 1 | no | — |
| 181 | C2×D7 | — | 6 | 1 | no | — |
| 182 | C2×D7 | — | 6 | 1 | no | — |
| 183 | C2×D7 | — | 6 | 1 | no | — |
| 184 | C2×D7 | — | 6 | 1 | no | — |
| 185 | C2×D7 | C2×S4 | 1 | 1 | yes | characteristic |
| 186 | C4×C7 | — | 6 | 1 | no | — |
| 187 | C4×C7 | — | 6 | 1 | no | — |
| 188 | C4×C7 | — | 6 | 1 | no | — |
| 189 | Dic7 | — | 3 | 1 | no | — |
| 190 | Dic7 | — | 6 | 1 | no | — |
| 191 | Dic7 | — | 6 | 1 | no | — |
| 192 | Dic7 | — | 6 | 1 | no | — |
| 193 | Dic7 | — | 6 | 1 | no | — |
| 194 | Dic7 | C2×S4 | 1 | 1 | yes | characteristic |
| 195 | C2×A4 | — | 2 | 1 | no | — |
| 196 | C2×A4 | — | 14 | 1 | no | — |
| 197 | C2×A4 | C22×D7 | 1 | 1 | yes | characteristic |
| 198 | S4 | — | 2 | 1 | no | — |
| 199 | C3×D4 | — | 28 | 1 | no | — |
| 200 | #67 | — | 4 | 1 | no | — |
| 201 | #67 | — | 28 | 1 | no | — |
| 202 | C2×Dic3 | — | 28 | 1 | no | — |
| 203 | C2×Dic3 | — | 28 | 1 | no | — |
| 204 | C4×D3 | — | 28 | 1 | no | — |
| 205 | Dic6 | — | 28 | 1 | no | — |
| 206 | C3×C7 | — | 4 | 1 | no | Hall |
| 207 | C24 | — | 7 | 1 | no | — |
| 208 | C24 | D3×D7 | 1 | 1 | yes | characteristic |
| 209 | #41 | — | 42 | 1 | no | — |
| 210 | #41 | — | 42 | 1 | no | — |
| 211 | #41 | — | 42 | 1 | no | — |
| 212 | #41 | — | 42 | 1 | no | — |
| 213 | C2×Q8 | — | 21 | 1 | no | — |
| 214 | C2×D4 | — | 3 | 1 | no | — |
| 215 | C2×D4 | — | 3 | 1 | no | — |
| 216 | C2×D4 | — | 3 | 1 | no | — |
| 217 | C2×D4 | — | 21 | 1 | no | — |
| 218 | C2×D4 | — | 21 | 1 | no | — |
| 219 | C2×D4 | — | 21 | 1 | no | — |
| 220 | C2×D4 | — | 21 | 1 | no | — |
| 221 | C2×D4 | — | 21 | 1 | no | — |
| 222 | C2×D4 | — | 21 | 1 | no | — |
| 223 | C22×C4 | — | 7 | 1 | no | — |
| 224 | C22×C4 | — | 21 | 1 | no | — |
| 225 | C22×C4 | — | 21 | 1 | no | — |
| 226 | C22×C4 | — | 21 | 1 | no | — |
| 227 | C22×C4 | — | 21 | 1 | no | — |
| 228 | C22×C4 | — | 21 | 1 | no | — |
| 229 | C4⋊C4 | — | 21 | 1 | no | — |
| 230 | C4⋊C4 | — | 21 | 1 | no | — |
| 231 | C4⋊C4 | — | 21 | 1 | no | — |
| 232 | C4⋊C4 | — | 21 | 1 | no | — |
| 233 | C22⋊C4 | — | 3 | 1 | no | — |
| 234 | C22⋊C4 | — | 3 | 1 | no | — |
| 235 | C22⋊C4 | — | 3 | 1 | no | — |
| 236 | C22⋊C4 | — | 21 | 1 | no | — |
| 237 | C22⋊C4 | — | 21 | 1 | no | — |
| 238 | C22⋊C4 | — | 21 | 1 | no | — |
| 239 | C22⋊C4 | — | 21 | 1 | no | — |
| 240 | C22⋊C4 | — | 21 | 1 | no | — |
| 241 | C22⋊C4 | — | 21 | 1 | no | — |
| 242 | C22⋊C4 | — | 21 | 1 | no | — |
| 243 | C22⋊C4 | — | 21 | 1 | no | — |
| 244 | C22⋊C4 | — | 21 | 1 | no | — |
| 245 | C42 | — | 21 | 1 | no | — |
| 246 | C2×C7 | — | 2 | 1 | no | — |
| 247 | C2×C7 | — | 3 | 1 | no | — |
| 248 | C2×C7 | — | 3 | 1 | no | — |
| 249 | C2×C7 | — | 6 | 1 | no | — |
| 250 | C2×C7 | — | 12 | 1 | no | — |
| 251 | C2×C7 | C22×S4 | 1 | 1 | yes | characteristic |
| 252 | D7 | — | 2 | 1 | no | — |
| 253 | D7 | — | 6 | 1 | no | — |
| 254 | C22×C3 | — | 4 | 1 | no | — |
| 255 | C22×C3 | — | 28 | 1 | no | — |
| 256 | C2×D3 | — | 4 | 1 | no | — |
| 257 | A4 | #1159 | 1 | 1 | yes | characteristic, complemented |
| 258 | C3×C4 | — | 28 | 1 | no | — |
| 259 | Dic3 | — | 4 | 1 | no | — |
| 260 | Dic3 | — | 28 | 1 | no | — |
| 261 | Dic3 | — | 28 | 1 | no | — |
| 262 | C23 | — | 2 | 1 | no | — |
| 263 | C23 | — | 3 | 1 | no | — |
| 264 | C23 | — | 3 | 1 | no | — |
| 265 | C23 | — | 3 | 1 | no | — |
| 266 | C23 | — | 6 | 1 | no | — |
| 267 | C23 | — | 14 | 1 | no | — |
| 268 | C23 | — | 21 | 1 | no | — |
| 269 | C23 | — | 21 | 1 | no | — |
| 270 | C23 | — | 42 | 1 | no | — |
| 271 | C23 | C2×D3×D7 | 1 | 1 | yes | characteristic |
| 272 | Q8 | — | 42 | 1 | no | — |
| 273 | Q8 | — | 42 | 1 | no | — |
| 274 | D4 | — | 6 | 1 | no | — |
| 275 | D4 | — | 6 | 1 | no | — |
| 276 | D4 | — | 6 | 1 | no | — |
| 277 | D4 | — | 6 | 1 | no | — |
| 278 | D4 | — | 7 | 1 | no | — |
| 279 | D4 | — | 12 | 1 | no | — |
| 280 | D4 | — | 21 | 1 | no | — |
| 281 | D4 | — | 21 | 1 | no | — |
| 282 | D4 | — | 21 | 1 | no | — |
| 283 | D4 | — | 42 | 1 | no | — |
| 284 | D4 | — | 42 | 1 | no | — |
| 285 | D4 | — | 42 | 1 | no | — |
| 286 | D4 | — | 84 | 1 | no | — |
| 287 | C2×C4 | — | 3 | 1 | no | — |
| 288 | C2×C4 | — | 3 | 1 | no | — |
| 289 | C2×C4 | — | 3 | 1 | no | — |
| 290 | C2×C4 | — | 21 | 1 | no | — |
| 291 | C2×C4 | — | 21 | 1 | no | — |
| 292 | C2×C4 | — | 21 | 1 | no | — |
| 293 | C2×C4 | — | 21 | 1 | no | — |
| 294 | C2×C4 | — | 21 | 1 | no | — |
| 295 | C2×C4 | — | 21 | 1 | no | — |
| 296 | C2×C4 | — | 42 | 1 | no | — |
| 297 | C2×C4 | — | 42 | 1 | no | — |
| 298 | C2×C4 | — | 42 | 1 | no | — |
| 299 | C2×C4 | — | 42 | 1 | no | — |
| 300 | C2×C4 | — | 42 | 1 | no | — |
| 301 | C2×C4 | — | 42 | 1 | no | — |
| 302 | C2×C4 | — | 84 | 1 | no | — |
| 303 | C2×C4 | — | 84 | 1 | no | — |
| 304 | C7 | #5914 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 305 | C2×C3 | — | 4 | 1 | no | — |
| 306 | C2×C3 | — | 8 | 1 | no | — |
| 307 | C2×C3 | — | 56 | 1 | no | — |
| 308 | D3 | — | 8 | 1 | no | — |
| 309 | C22 | — | 3 | 1 | no | — |
| 310 | C22 | — | 3 | 1 | no | — |
| 311 | C22 | — | 3 | 1 | no | — |
| 312 | C22 | — | 6 | 1 | no | — |
| 313 | C22 | — | 6 | 1 | no | — |
| 314 | C22 | — | 6 | 1 | no | — |
| 315 | C22 | — | 6 | 1 | no | — |
| 316 | C22 | — | 6 | 1 | no | — |
| 317 | C22 | — | 6 | 1 | no | — |
| 318 | C22 | — | 6 | 1 | no | — |
| 319 | C22 | — | 7 | 1 | no | — |
| 320 | C22 | — | 21 | 1 | no | — |
| 321 | C22 | — | 42 | 1 | no | — |
| 322 | C22 | — | 42 | 1 | no | — |
| 323 | C22 | — | 42 | 1 | no | — |
| 324 | C22 | — | 42 | 1 | no | — |
| 325 | C22 | #66684 | 1 | 1 | yes | characteristic, complemented |
| 326 | C22 | D7×S4 | 1 | 1 | yes | characteristic |
| 327 | C4 | — | 6 | 1 | no | — |
| 328 | C4 | — | 6 | 1 | no | — |
| 329 | C4 | — | 6 | 1 | no | — |
| 330 | C4 | — | 7 | 1 | no | — |
| 331 | C4 | — | 21 | 1 | no | — |
| 332 | C4 | — | 42 | 1 | no | — |
| 333 | C4 | — | 42 | 1 | no | — |
| 334 | C4 | — | 42 | 1 | no | — |
| 335 | C4 | — | 42 | 1 | no | — |
| 336 | C3 | — | 4 | 1 | no | Sylow |
| 337 | C2 | — | 2 | 1 | no | — |
| 338 | C2 | — | 3 | 1 | no | — |
| 339 | C2 | — | 3 | 1 | no | — |
| 340 | C2 | — | 6 | 1 | no | — |
| 341 | C2 | — | 12 | 1 | no | — |
| 342 | C2 | — | 14 | 1 | no | — |
| 343 | C2 | — | 42 | 1 | no | — |
| 344 | C2 | C2×D7×S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D7×S4 |
| commutator, cosocle | C2×C7×A4 | C23 |
| Fitting | C24×C7 | C2×D3 |
| socle | C23×C7 | C22×D3 |
| hypercenter | C22 | D7×S4 |
| hypocenter | C7×A4 | #41 |
| LCS | G ▷ C2×C7×A4 ▷ C7×A4 | |
| UCS | C1 ◁ C2 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. A4×C22⋊D7 | C2 | semidirect |
| 2. C2×C7⋊SL(2,ℤ/4) | C2 | semidirect |
| 3. C7×GL(2,ℤ/4) | C2 | semidirect |
| 4. #10621482 | C2 | semidirect |
| 5. D7×SL(2,ℤ/4) | C2 | semidirect |
| 6. S4×Dic7 | C2 | semidirect |
| 7. #10621477 | C2 | semidirect |
| 17. C22×C22⋊D7 | D3 | semidirect |
| 85. GL(2,ℤ/4) | D7 | semidirect |
| 93. C7×A4 | #41 | semidirect |
| 124. C22⋊D7 | S4 | semidirect |
| 178. C22×C7 | #237 | semidirect |
| 257. A4 | #1159 | semidirect |
| 304. C7 | #5914 | semidirect |
| 325. C22 | #66684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×C22⋊D7 | 2 |
| C2×C7⋊SL(2,ℤ/4) | 2 |
| C7×GL(2,ℤ/4) | 2 |
| #10621482 | 2 |
| D7×SL(2,ℤ/4) | 2 |
| S4×Dic7 | 2 |
| #10621477 | 2 |
| #90282 | 3 |
| #66684 | 4 |
| #5914 | 7 |