Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
264 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 222. C7 | #10688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11728273 | 2 |
| #11727239 | 2 |
| C7×#1303 | 2 |
| #11725551 | 2 |
| #11725546 | 2 |
| #11725520 | 2 |
| #11725426 | 2 |
| #10688 | 7 |