Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
410 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 2. #14544992 | C2 | semidirect |
| 4. #14543833 | C2 | semidirect |
| 10. #11763706 | C4 | semidirect |
| 11. #11763705 | C4 | semidirect |
| 18. C2×#10587483 | C4 | semidirect |
| 19. C2×#10587469 | C4 | semidirect |
| 21. C2×C16×D17 | C4 | semidirect |
| 23. C22×C16×C17 | C4 | semidirect |
| 143. C22×C16 | #595 | semidirect |
| 190. C17 | #12613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545021 | 2 |
| #14544992 | 2 |
| #14544539 | 2 |
| #14543833 | 2 |
| C2×#11763225 | 2 |
| #12613 | 17 |