Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
156 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 26 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×#994 | C2 | semidirect |
| 2. C7×#986 | C2 | semidirect |
| 3. C7×GU(2,𝔽3) | C2 | semidirect |
| 9. C7×H(5,𝔽2) | D3 | semidirect |
| 16. #5429 | C7 | direct (N × H) |
| 19. C7×SL(2,𝔽3) | D4 | semidirect |
| 35. #994 | C2×C7 | semidirect |
| 36. #986 | C2×C7 | semidirect |
| 37. GU(2,𝔽3) | C2×C7 | semidirect |
| 64. H(5,𝔽2) | D3×C7 | semidirect |
| 82. SL(2,𝔽3) | C7×D4 | semidirect |
| 122. C7 | #5429 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#994 | 2 |
| C7×#986 | 2 |
| C7×GU(2,𝔽3) | 2 |
| C7×#453 | 3 |
| C7×#215 | 4 |
| #5429 | 7 |