Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
444 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 106 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. #14544440 | C2 | semidirect |
| 4. C8×#63243 | C2 | semidirect |
| 5. #14543677 | C2 | semidirect |
| 6. #14543671 | C2 | semidirect |
| 14. #11763666 | C4 | semidirect |
| 15. #11763665 | C4 | semidirect |
| 21. #11762940 | C4 | semidirect |
| 22. #11762886 | C4 | semidirect |
| 25. C8×D68 | C4 | semidirect |
| 30. C8×Q8×C17 | C4 | semidirect |
| 176. C8×Q8 | #595 | semidirect |
| 245. C17 | #8247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544440 | 2 |
| #14544236 | 2 |
| #14544157 | 2 |
| C8×#63243 | 2 |
| #14543677 | 2 |
| #14543671 | 2 |
| #14537761 | 2 |
| #8247 | 17 |