Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
434 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. C7×#2110 | C2 | semidirect |
| 5. C2×#89312 | C2 | semidirect |
| 6. #11729199 | C2 | semidirect |
| 7. #11727650 | C2 | semidirect |
| 18. #89471 | C4 | semidirect |
| 19. #89468 | C4 | semidirect |
| 73. #2110 | D7 | semidirect |
| 317. C7 | #13216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736021 | 2 |
| C7×#2110 | 2 |
| #11729204 | 2 |
| #11729202 | 2 |
| C2×#89312 | 2 |
| #11729199 | 2 |
| #11727650 | 2 |
| #13216 | 7 |