Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
458 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 80 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. #14545685 | C2 | semidirect |
| 2. #14544556 | C2 | semidirect |
| 5. #14543677 | C2 | semidirect |
| 6. #14543636 | C2 | semidirect |
| 25. #11763101 | C4 | semidirect |
| 26. #11763010 | C4 | semidirect |
| 27. #11763009 | C4 | semidirect |
| 32. C17×#477 | C4 | semidirect |
| 209. #477 | #595 | semidirect |
| 285. C17 | #9164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545685 | 2 |
| #14544556 | 2 |
| #14544255 | 2 |
| #14544165 | 2 |
| #14543677 | 2 |
| #14543636 | 2 |
| #14538908 | 2 |
| #9164 | 17 |