Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
316 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 72 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. #14545140 | C2 | semidirect |
| 4. #108×#595 | C2 | semidirect |
| 5. #14543863 | C2 | semidirect |
| 6. #14543827 | C2 | semidirect |
| 23. #11762625 | C4 | semidirect |
| 24. #11762623 | C4 | semidirect |
| 25. #11762621 | C4 | semidirect |
| 26. C17×#362 | C4 | semidirect |
| 169. #362 | #595 | semidirect |
| 216. C17 | #13137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545140 | 2 |
| #14545100 | 2 |
| #14544935 | 2 |
| #108×#595 | 2 |
| #14543863 | 2 |
| #14543827 | 2 |
| #14530532 | 2 |
| #13137 | 17 |