Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
264 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 72 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. #10621376 | C2 | semidirect |
| 2. #10620997 | C2 | semidirect |
| 4. C7×#809 | C2 | semidirect |
| 5. C3×#6382 | C2 | semidirect |
| 6. #10620503 | C2 | semidirect |
| 7. #10620489 | C2 | semidirect |
| 20. #66562 | C4 | semidirect |
| 27. #6382 | D3 | semidirect |
| 36. D84 | C2×C4 | semidirect |
| 39. C7×D12 | C2×C4 | semidirect |
| 42. C3×C7⋊C8 | C2×C4 | semidirect |
| 62. #809 | D7 | semidirect |
| 91. C7⋊C8 | C4×D3 | semidirect |
| 139. D12 | C4×D7 | semidirect |
| 144. C3×C7 | #442 | semidirect |
| 190. C7 | #4869 | semidirect |
| 209. C3 | #89557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621376 | 2 |
| #10620997 | 2 |
| C2×#66562 | 2 |
| C7×#809 | 2 |
| C3×#6382 | 2 |
| #10620503 | 2 |
| #10620489 | 2 |
| #89557 | 3 |
| #4869 | 7 |