Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
280 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 68 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. C2×C7×D24 | C2 | semidirect |
| 2. #10621013 | C2 | semidirect |
| 3. D12×Dic7 | C2 | semidirect |
| 4. C2×#66562 | C2 | semidirect |
| 5. #10620660 | C2 | semidirect |
| 6. C3×Dic7⋊C8 | C2 | semidirect |
| 7. #10620502 | C2 | semidirect |
| 28. Dic7⋊C8 | D3 | semidirect |
| 40. C7×D12 | D4 | semidirect |
| 62. C2×D24 | D7 | semidirect |
| 82. C3×Dic7 | D8 | semidirect |
| 142. Dic7 | D24 | semidirect |
| 157. D12 | C22⋊D7 | semidirect |
| 161. C3×C7 | #459 | semidirect |
| 214. C7 | #4843 | semidirect |
| 236. C3 | #89922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×D24 | 2 |
| #10621013 | 2 |
| D12×Dic7 | 2 |
| C2×#66562 | 2 |
| #10620660 | 2 |
| C3×Dic7⋊C8 | 2 |
| #10620502 | 2 |
| #89922 | 3 |
| #4843 | 7 |