Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
492 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 96 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. #14544969 | C2 | semidirect |
| 3. C4×#10587532 | C2 | semidirect |
| 4. #14544343 | C2 | semidirect |
| 5. #14544134 | C2 | semidirect |
| 20. #11763205 | C4 | semidirect |
| 21. #11763183 | C4 | semidirect |
| 22. #11763156 | C4 | semidirect |
| 26. C17×#487 | C4 | semidirect |
| 142. #3622 | #104 | semidirect |
| 172. #487 | #595 | semidirect |
| 231. C17 | #9851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544969 | 2 |
| #14544917 | 2 |
| C4×#10587532 | 2 |
| #14544343 | 2 |
| #14544134 | 2 |
| #14544131 | 2 |
| #14539346 | 2 |
| #9851 | 17 |