Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
314 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 314 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. #14545132 | C2 | semidirect |
| 4. #14544593 | C2 | semidirect |
| 5. #14543853 | C2 | semidirect |
| 6. #14543830 | C2 | semidirect |
| 23. #11762626 | C4 | semidirect |
| 24. #11762624 | C4 | semidirect |
| 25. #11762622 | C4 | semidirect |
| 26. C17×#361 | C4 | semidirect |
| 169. #361 | #595 | semidirect |
| 213. C17 | #13140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545132 | 2 |
| #14545105 | 2 |
| #14544939 | 2 |
| #14544593 | 2 |
| #14543853 | 2 |
| #14543830 | 2 |
| #14530530 | 2 |
| #13140 | 17 |