Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
430 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 100 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. #14545117 | C2 | semidirect |
| 3. #14544721 | C2 | semidirect |
| 4. #14543855 | C2 | semidirect |
| 15. Q16×Dic17 | C4 | semidirect |
| 18. C4×D136 | C4 | semidirect |
| 19. #11762891 | C4 | semidirect |
| 23. C4×Q16×C17 | C4 | semidirect |
| 177. C4×Q16 | #595 | semidirect |
| 237. C17 | #12817 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545117 | 2 |
| C2×#11763726 | 2 |
| #14544721 | 2 |
| #14543855 | 2 |
| C4×#10587605 | 2 |
| #12817 | 17 |