Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
826 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 136 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. C4×#10587543 | C2 | semidirect |
| 2. C2×#11763661 | C2 | semidirect |
| 3. #14543962 | C2 | semidirect |
| 12. C2×#10587560 | C4 | semidirect |
| 19. #11762710 | C4 | semidirect |
| 20. C17×#384 | C4 | semidirect |
| 54. #10587543 | D4 | semidirect |
| 212. C4×C17 | #327 | semidirect |
| 227. #384 | #595 | semidirect |
| 279. C17 | #9680 | semidirect |
| 434. C4 | #11763661 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#10587543 | 2 |
| C2×#11763661 | 2 |
| #14543962 | 2 |
| #14537130 | 2 |
| #9680 | 17 |