Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
456 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 86 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. #14544663 | C2 | semidirect |
| 2. #14544661 | C2 | semidirect |
| 4. #14543684 | C2 | semidirect |
| 14. C2×#10587634 | C4 | semidirect |
| 21. #11762835 | C4 | semidirect |
| 23. #11762767 | C4 | semidirect |
| 24. C17×#408 | C4 | semidirect |
| 197. #408 | #595 | semidirect |
| 253. C17 | #8627 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544663 | 2 |
| #14544661 | 2 |
| #14544199 | 2 |
| #14543684 | 2 |
| #14537481 | 2 |
| #8627 | 17 |