Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
412 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 4. #11727888 | C2 | semidirect |
| 5. #11725506 | C2 | semidirect |
| 267. C7 | #12810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740721 | 2 |
| C7×#2132 | 2 |
| #11729574 | 2 |
| #11727888 | 2 |
| #11725506 | 2 |
| #12810 | 7 |