Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
770 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 108 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. #14544511 | C2 | semidirect |
| 2. C2×#11763661 | C2 | semidirect |
| 3. #14543960 | C2 | semidirect |
| 12. C2×#10587560 | C4 | semidirect |
| 19. #11762710 | C4 | semidirect |
| 20. C17×#384 | C4 | semidirect |
| 50. #10587543 | D4 | semidirect |
| 205. #384 | #595 | semidirect |
| 252. C17 | #9684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544511 | 2 |
| C2×#11763661 | 2 |
| #14543960 | 2 |
| #14537130 | 2 |
| #9684 | 17 |