Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
306 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 252. C7 | #10610 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1997 | 2 |
| #11729529 | 2 |
| C2×#89342 | 2 |
| #11728247 | 2 |
| #11727629 | 2 |
| #11727604 | 2 |
| #11725517 | 2 |
| #10610 | 7 |