Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
412 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 29. C17×#95 | C8 | semidirect |
| 196. #95 | #3624 | semidirect |
| 197. C17 | #7123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14543622 | 2 |
| #14527049 | 2 |
| #7123 | 17 |