Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
272 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11725591 | C2 | semidirect |
| 181. C7 | #11914 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3177 | 2 |
| #11727640 | 2 |
| #11727638 | 2 |
| #11725591 | 2 |
| #11914 | 7 |