Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
296 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 79 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×#2241 | C2 | semidirect |
| 2. #11729136 | C2 | semidirect |
| 5. #11729052 | C2 | semidirect |
| 7. #11725305 | C2 | semidirect |
| 50. #2241 | D7 | semidirect |
| 114. C7⋊C8 | SD32 | semidirect |
| 199. C7 | #12526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2241 | 2 |
| #11729136 | 2 |
| #11729113 | 2 |
| #11729067 | 2 |
| #11729052 | 2 |
| #11726815 | 2 |
| #11725305 | 2 |
| #12526 | 7 |