Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
366 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 301. C7 | #10471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739876 | 2 |
| C7×#1805 | 2 |
| #11729378 | 2 |
| #11728191 | 2 |
| #11728176 | 2 |
| #11727300 | 2 |
| #11725437 | 2 |
| #10471 | 7 |