Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
260 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 62 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. #10621378 | C2 | semidirect |
| 2. #10621028 | C2 | semidirect |
| 3. C2×#66562 | C2 | semidirect |
| 4. C2×#66559 | C2 | semidirect |
| 5. C7×#809 | C2 | semidirect |
| 6. C3×#6382 | C2 | semidirect |
| 7. #10620503 | C2 | semidirect |
| 28. #6382 | D3 | semidirect |
| 45. C3×C7⋊C8 | D4 | semidirect |
| 66. #809 | D7 | semidirect |
| 99. C7⋊C8 | D12 | semidirect |
| 158. C3×C7 | #469 | semidirect |
| 210. C7 | #4865 | semidirect |
| 232. C3 | #89554 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621378 | 2 |
| #10621028 | 2 |
| C2×#66562 | 2 |
| C2×#66559 | 2 |
| C7×#809 | 2 |
| C3×#6382 | 2 |
| #10620503 | 2 |
| #89554 | 3 |
| #4865 | 7 |