Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
508 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 82 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. #14545644 | C2 | semidirect |
| 2. #14544554 | C2 | semidirect |
| 3. #14544255 | C2 | semidirect |
| 4. #14544165 | C2 | semidirect |
| 5. #14543677 | C2 | semidirect |
| 6. #14543636 | C2 | semidirect |
| 25. #11763096 | C4 | semidirect |
| 26. #11763005 | C4 | semidirect |
| 27. #11763004 | C4 | semidirect |
| 32. C17×#476 | C4 | semidirect |
| 224. #476 | #595 | semidirect |
| 302. C17 | #9163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545644 | 2 |
| #14544554 | 2 |
| #14544255 | 2 |
| #14544165 | 2 |
| #14543677 | 2 |
| #14543636 | 2 |
| #14538877 | 2 |
| #9163 | 17 |