Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C3⋊(C7⋊C8) | C2 | semidirect |
| 3. C2×D7×C3⋊C8 | C2 | semidirect |
| 4. C7×#830 | C2 | semidirect |
| 5. Dic7⋊(C3⋊C8) | C2 | semidirect |
| 6. (C2×D7)⋊(C3⋊C8) | C2 | semidirect |
| 7. C3⋊C8×Dic7 | C2 | semidirect |
| 36. C3×C22⋊D7 | C8 | semidirect |
| 43. C3⋊(C7⋊C8) | D4 | semidirect |
| 63. #830 | D7 | semidirect |
| 68. C22×C3×C7 | C2×C8 | semidirect |
| 72. C2×C3×D7 | C2×C8 | semidirect |
| 78. C3×Dic7 | C2×C8 | semidirect |
| 86. C22⋊D7 | C3⋊C8 | semidirect |
| 123. C22×C7 | C2×C3⋊C8 | semidirect |
| 127. C2×D7 | C2×C3⋊C8 | semidirect |
| 133. Dic7 | C2×C3⋊C8 | semidirect |
| 150. C3×C7 | C8×D4 | semidirect |
| 174. C22×C3 | C8×D7 | semidirect |
| 198. C7 | D4×C3⋊C8 | semidirect |
| 209. C22 | D7×C3⋊C8 | semidirect |
| 217. C3 | (C22⋊D7)⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊(C7⋊C8) | 2 |
| C3×C4×C22⋊D7 | 2 |
| C2×D7×C3⋊C8 | 2 |
| C7×#830 | 2 |
| Dic7⋊(C3⋊C8) | 2 |
| (C2×D7)⋊(C3⋊C8) | 2 |
| C3⋊C8×Dic7 | 2 |
| (C22⋊D7)⋊C8 | 3 |
| D4×C3⋊C8 | 7 |