Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
284 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
| 3. #11729114 | C2 | semidirect |
| 4. #11729066 | C2 | semidirect |
| 7. #11725305 | C2 | semidirect |
| 49. #2241 | D7 | semidirect |
| 197. C7 | #12530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2241 | 2 |
| #11729135 | 2 |
| #11729114 | 2 |
| #11729066 | 2 |
| #11729051 | 2 |
| #11726815 | 2 |
| #11725305 | 2 |
| #12530 | 7 |