Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
204 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 180. C7 | #12079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11726836 | 2 |
| #11726278 | 2 |
| #11726271 | 2 |
| C7×#1368 | 2 |
| #11725318 | 2 |
| #11725272 | 2 |
| #12079 | 7 |