Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
278 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 254. C7 | #12296 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3261 | 2 |
| #11728833 | 2 |
| #11728832 | 2 |
| #11728286 | 2 |
| #11725583 | 2 |
| #11725524 | 2 |
| #12296 | 7 |