Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
396 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 80 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. C22×C7×D12 | C2 | semidirect |
| 2. #10621413 | C2 | semidirect |
| 3. C2×#66562 | C2 | semidirect |
| 4. C3×C22⋊(C7⋊C8) | C2 | semidirect |
| 5. #10620502 | C2 | semidirect |
| 10. C2×D84 | C22 | semidirect |
| 15. C4⋊Dic21 | C22 | semidirect |
| 16. C2×C3×C7⋊C8 | C22 | semidirect |
| 22. C22⋊(C7⋊C8) | D3 | semidirect |
| 38. C7×D12 | D4 | semidirect |
| 50. C2×C7⋊C8 | C2×D3 | semidirect |
| 51. C22×D12 | D7 | semidirect |
| 58. C22×C3×C7 | D8 | semidirect |
| 115. C22×C7 | D24 | semidirect |
| 137. D12 | C22⋊D7 | semidirect |
| 139. C3×C7 | #447 | semidirect |
| 159. C22×C3 | #1141 | semidirect |
| 187. C7 | #4732 | semidirect |
| 203. C22 | #66562 | semidirect |
| 208. C3 | #89989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D12 | 2 |
| #10621413 | 2 |
| C2×#66562 | 2 |
| C3×C22⋊(C7⋊C8) | 2 |
| #10620502 | 2 |
| #89989 | 3 |
| #4732 | 7 |