Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
416 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 416 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 |
|---|---|---|
| 1. #14545012 | C2 | semidirect |
| 2. #14544661 | C2 | semidirect |
| 3. #14543773 | C2 | semidirect |
| 4. #14543771 | C2 | semidirect |
| 12. C2×#10587590 | C4 | semidirect |
| 15. #11763051 | C4 | semidirect |
| 17. #11763046 | C4 | semidirect |
| 22. C17×#427 | C4 | semidirect |
| 184. #427 | #595 | semidirect |
| 234. C17 | #11890 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545012 | 2 |
| #14544661 | 2 |
| #14543773 | 2 |
| #14543771 | 2 |
| #14538366 | 2 |
| #11890 | 17 |