Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
274 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 83 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×#2161 | C2 | semidirect |
| 5. #11725622 | C2 | semidirect |
| 6. #11725540 | C2 | semidirect |
| 7. #11725536 | C2 | semidirect |
| 53. #2161 | D7 | semidirect |
| 247. C7 | #13497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2161 | 2 |
| #11729191 | 2 |
| #11728474 | 2 |
| #11728472 | 2 |
| #11725622 | 2 |
| #11725540 | 2 |
| #11725536 | 2 |
| #13497 | 7 |