Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
954 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 163 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. #11743299 | C2 | semidirect |
| 3. #11740766 | C2 | semidirect |
| 4. #11729564 | C2 | semidirect |
| 5. #11729061 | C2 | semidirect |
| 6. #11729038 | C2 | semidirect |
| 7. #11729024 | C2 | semidirect |
| 8. #11729023 | C2 | semidirect |
| 9. #11727492 | C2 | semidirect |
| 359. C7 | #18688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11743299 | 2 |
| C7×#3147 | 2 |
| #11740766 | 2 |
| #11729564 | 2 |
| #11729061 | 2 |
| #11729038 | 2 |
| #11729024 | 2 |
| #11729023 | 2 |
| #11727492 | 2 |
| #18688 | 7 |