Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
428 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 3. M32×#595 | C2 | semidirect |
| 4. #14544589 | C2 | semidirect |
| 5. #14543865 | C2 | semidirect |
| 6. #14543863 | C2 | semidirect |
| 12. #11763853 | C4 | semidirect |
| 13. #11763853 | C4 | semidirect |
| 19. #11763726 | C4 | semidirect |
| 26. #11762625 | C4 | semidirect |
| 27. #11762623 | C4 | semidirect |
| 28. #11762621 | C4 | semidirect |
| 29. C17×#362 | C4 | semidirect |
| 189. #362 | #595 | semidirect |
| 243. C17 | #12646 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763853 | 2 |
| #14545106 | 2 |
| M32×#595 | 2 |
| #14544589 | 2 |
| #14543865 | 2 |
| #14543863 | 2 |
| #14530532 | 2 |
| #12646 | 17 |