Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
172 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 42 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 |
|---|---|---|
| 2. C3×C7×#99 | C2 | semidirect |
| 3. C7×#834 | C2 | semidirect |
| 8. C2×C7×D12 | C4 | semidirect |
| 11. C4×C7×Dic3 | C4 | semidirect |
| 14. C7×#99 | D3 | semidirect |
| 15. #4474 | C7 | direct (N × H) |
| 35. C3×#99 | C2×C7 | semidirect |
| 36. #834 | C2×C7 | semidirect |
| 64. C2×D12 | C4×C7 | semidirect |
| 67. C4×Dic3 | C4×C7 | semidirect |
| 75. #99 | D3×C7 | semidirect |
| 99. C3×C7 | #353 | semidirect |
| 135. C7 | #4474 | direct (N × H) |
| 153. C3 | C7×#353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#940 | 2 |
| C3×C7×#99 | 2 |
| C7×#834 | 2 |
| C7×#353 | 3 |
| #4474 | 7 |