Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 78 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. C7×#893 | C2 | semidirect |
| 2. #10620990 | C2 | semidirect |
| 4. #10620648 | C2 | semidirect |
| 5. C3×#6381 | C2 | semidirect |
| 6. #10620501 | C2 | semidirect |
| 7. Dic3×C7⋊C8 | C2 | semidirect |
| 20. #66562 | C4 | semidirect |
| 26. #6381 | D3 | semidirect |
| 34. D84 | C2×C4 | semidirect |
| 38. C7×D12 | C2×C4 | semidirect |
| 43. C3×C7⋊C8 | C2×C4 | semidirect |
| 58. #893 | D7 | semidirect |
| 75. C7×Dic3 | D8 | semidirect |
| 91. C7⋊C8 | C4×D3 | semidirect |
| 139. D12 | C4×D7 | semidirect |
| 144. C3×C7 | C4×D8 | semidirect |
| 174. Dic3 | #1141 | semidirect |
| 190. C7 | #4872 | semidirect |
| 209. C3 | C4×#1141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#893 | 2 |
| #10620990 | 2 |
| C2×#66562 | 2 |
| #10620648 | 2 |
| C3×#6381 | 2 |
| #10620501 | 2 |
| Dic3×C7⋊C8 | 2 |
| C4×#1141 | 3 |
| #4872 | 7 |