Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 2. D12×Dic7 | C2 | semidirect |
| 3. #10620657 | C2 | semidirect |
| 4. C3×C8×Dic7 | C2 | semidirect |
| 5. #10620502 | C2 | semidirect |
| 11. C7×D24 | C4 | semidirect |
| 19. C8×Dic7 | D3 | semidirect |
| 25. C7×D12 | C2×C4 | semidirect |
| 29. C3×C7×C8 | C2×C4 | semidirect |
| 52. C3×Dic7 | D8 | semidirect |
| 62. C7×C8 | C4×D3 | semidirect |
| 71. D24 | Dic7 | direct (N × H) |
| 89. Dic7 | D24 | direct (N × H) |
| 96. D12 | C2×Dic7 | semidirect |
| 99. C3×C8 | C2×Dic7 | semidirect |
| 100. C3×C7 | C4×D8 | semidirect |
| 131. C8 | D3×Dic7 | semidirect |
| 132. C7 | C4×D24 | semidirect |
| 146. C3 | D8×Dic7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×D24 | 2 |
| D12×Dic7 | 2 |
| #10620657 | 2 |
| C3×C8×Dic7 | 2 |
| #10620502 | 2 |
| D8×Dic7 | 3 |
| C4×D24 | 7 |