Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
526 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 3. #11725436 | C2 | semidirect |
| 184. C7 | #8721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2285 | 2 |
| #11729283 | 2 |
| #11725436 | 2 |
| #8721 | 7 |