Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
184 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 59 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×#2258 | C2 | semidirect |
| 2. #11729210 | C2 | semidirect |
| 4. C2×#89244 | C2 | semidirect |
| 5. #11725411 | C2 | semidirect |
| 6. #11725410 | C2 | semidirect |
| 7. #11725399 | C2 | semidirect |
| 45. #2258 | D7 | semidirect |
| 170. C7 | #13702 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2258 | 2 |
| #11729210 | 2 |
| #11729208 | 2 |
| C2×#89244 | 2 |
| #11725411 | 2 |
| #11725410 | 2 |
| #11725399 | 2 |
| #13702 | 7 |