Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
350 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 160 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 |
|---|---|---|
| 9. #11763700 | C4 | semidirect |
| 10. #11763699 | C4 | semidirect |
| 11. #11763698 | C4 | semidirect |
| 12. #11763697 | C4 | semidirect |
| 13. #11763696 | C4 | semidirect |
| 14. #11763695 | C4 | semidirect |
| 15. C4×#63216 | C4 | semidirect |
| 16. C16×#595 | C4 | semidirect |
| 22. #11762587 | C4 | semidirect |
| 23. #11762586 | C4 | semidirect |
| 24. C17×#347 | C4 | semidirect |
| 112. #347 | #595 | semidirect |
| 148. C17 | #12542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545004 | 2 |
| #14544996 | 2 |
| #14544994 | 2 |
| #14544506 | 2 |
| #14530387 | 2 |
| #12542 | 17 |