Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
412 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 27. #89260 | C4 | semidirect |
| 321. C7 | #8912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11731606 | 2 |
| #11727581 | 2 |
| #11727570 | 2 |
| C2×#89260 | 2 |
| #11727302 | 2 |
| C7×#1295 | 2 |
| #11725465 | 2 |
| #8912 | 7 |