Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
264 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 84 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. #10620656 | C2 | semidirect |
| 4. C3×#6389 | C2 | semidirect |
| 5. #10620502 | C2 | semidirect |
| 11. C7×D24 | C4 | semidirect |
| 19. #6389 | D3 | semidirect |
| 25. C7×D12 | C2×C4 | semidirect |
| 28. C3×C7×C8 | C2×C4 | semidirect |
| 59. C7×C8 | C4×D3 | semidirect |
| 68. D24 | Dic7 | semidirect |
| 90. D12 | C2×Dic7 | semidirect |
| 93. C3×C8 | C2×Dic7 | semidirect |
| 94. C3×C7 | #442 | semidirect |
| 122. C8 | D3×Dic7 | semidirect |
| 123. C7 | #4711 | semidirect |
| 135. C3 | #89924 | 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 |
| #10620656 | 2 |
| C3×#6389 | 2 |
| #10620502 | 2 |
| #89924 | 3 |
| #4711 | 7 |