Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
460 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 97 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. #11728520 | C2 | semidirect |
| 5. #11728503 | C2 | semidirect |
| 6. #11728282 | C2 | semidirect |
| 7. #11725520 | C2 | semidirect |
| 320. C7 | #10443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89847 | 2 |
| C7×#1545 | 2 |
| #11729513 | 2 |
| #11728520 | 2 |
| #11728503 | 2 |
| #11728282 | 2 |
| #11725520 | 2 |
| #10443 | 7 |