Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
558 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 558 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. #14545708 | C2 | semidirect |
| 2. #14544951 | C2 | semidirect |
| 3. #14544659 | C2 | semidirect |
| 4. #14544292 | C2 | semidirect |
| 5. #14543680 | C2 | semidirect |
| 6. #14543653 | C2 | semidirect |
| 25. #11763009 | C4 | semidirect |
| 27. #11763005 | C4 | semidirect |
| 29. #11763001 | C4 | semidirect |
| 32. C17×#460 | C4 | semidirect |
| 249. #460 | #595 | semidirect |
| 329. C17 | #9322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545708 | 2 |
| #14544951 | 2 |
| #14544659 | 2 |
| #14544292 | 2 |
| #14543680 | 2 |
| #14543653 | 2 |
| #14538261 | 2 |
| #9322 | 17 |