Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
534 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 94 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. Q8×#63247 | C2 | semidirect |
| 4. #14544112 | C2 | semidirect |
| 5. #14543654 | C2 | semidirect |
| 6. #14543629 | C2 | semidirect |
| 121. #63247 | SD16 | semidirect |
| 166. Q8×C17 | #100 | semidirect |
| 324. C17 | #9254 | semidirect |
| 405. Q8 | #10587553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#63247 | 2 |
| #14544926 | 2 |
| #14544291 | 2 |
| #14544112 | 2 |
| #14543654 | 2 |
| #14543629 | 2 |
| C2×#11763007 | 2 |
| #9254 | 17 |