Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
234 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 4. #11725817 | C2 | semidirect |
| 5. #11725281 | C2 | semidirect |
| 6. #11725280 | C2 | semidirect |
| 7. #11725245 | C2 | semidirect |
| 200. C7 | #12422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×C8×D8 | 2 |
| #11728646 | 2 |
| #11728640 | 2 |
| #11725817 | 2 |
| #11725281 | 2 |
| #11725280 | 2 |
| #11725245 | 2 |
| #12422 | 7 |