Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
318 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 17. #11762584 | C4 | semidirect |
| 18. #11762584 | C4 | semidirect |
| 19. C4×#63214 | C4 | semidirect |
| 20. C4×C16×C17 | C4 | semidirect |
| 121. C4×C16 | #595 | semidirect |
| 151. C17 | #12904 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763734 | 2 |
| C2×#11763733 | 2 |
| #14544724 | 2 |
| #14544721 | 2 |
| C4×#10587469 | 2 |
| #12904 | 17 |