Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
360 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 74 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. #14545154 | C2 | semidirect |
| 2. #14544007 | C2 | semidirect |
| 3. #14543748 | C2 | semidirect |
| 4. #14543746 | C2 | semidirect |
| 7. #11763731 | C22 | semidirect |
| 11. #11763650 | C22 | semidirect |
| 12. C8×#3624 | C22 | semidirect |
| 62. Q16×C17 | M16 | semidirect |
| 66. D8×C17 | M16 | semidirect |
| 172. C17 | #11669 | semidirect |
| 184. Q16 | #63247 | semidirect |
| 188. D8 | #63247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545154 | 2 |
| #14544007 | 2 |
| #14543748 | 2 |
| #14543746 | 2 |
| #14537694 | 2 |
| #11669 | 17 |