Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
396 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 94 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. C7×#930 | C2 | semidirect |
| 3. C2×C7×D24 | C2 | semidirect |
| 4. C3×C7×C22⋊C8 | C2 | semidirect |
| 5. C7×#821 | C2 | semidirect |
| 13. C2×C7×D12 | C22 | semidirect |
| 14. C2×C3×C7×C8 | C22 | semidirect |
| 16. C7×C4⋊Dic3 | C22 | semidirect |
| 22. C7×C22⋊C8 | D3 | semidirect |
| 23. #4732 | C7 | direct (N × H) |
| 38. C7×D12 | D4 | semidirect |
| 48. C2×C7×C8 | C2×D3 | semidirect |
| 51. C22×D12 | C2×C7 | semidirect |
| 52. #930 | C2×C7 | semidirect |
| 53. C2×D24 | C2×C7 | semidirect |
| 54. C3×C22⋊C8 | C2×C7 | semidirect |
| 55. #821 | C2×C7 | semidirect |
| 58. C22×C3×C7 | D8 | semidirect |
| 93. C2×D12 | C22×C7 | semidirect |
| 94. C2×C3×C8 | C22×C7 | semidirect |
| 96. C4⋊Dic3 | C22×C7 | semidirect |
| 108. C22⋊C8 | D3×C7 | semidirect |
| 118. C22×C7 | D24 | semidirect |
| 137. D12 | C7×D4 | semidirect |
| 139. C3×C7 | #447 | semidirect |
| 148. C2×C8 | C2×D3×C7 | semidirect |
| 159. C22×C3 | C7×D8 | semidirect |
| 187. C7 | #4732 | direct (N × H) |
| 203. C22 | C7×D24 | semidirect |
| 208. C3 | C7×#447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D12 | 2 |
| C7×#930 | 2 |
| C2×C7×D24 | 2 |
| C3×C7×C22⋊C8 | 2 |
| C7×#821 | 2 |
| C7×#447 | 3 |
| #4732 | 7 |