Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
572 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 124 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. #14544501 | C2 | semidirect |
| 2. C4×#10587542 | C2 | semidirect |
| 4. #14543660 | C2 | semidirect |
| 12. #11763665 | C4 | semidirect |
| 52. #10587542 | C2×C4 | semidirect |
| 53. #10587542 | C2×C4 | semidirect |
| 242. C17 | #8226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544501 | 2 |
| C4×#10587542 | 2 |
| C2×#11763665 | 2 |
| #14543660 | 2 |
| C4×#10587633 | 2 |
| #8226 | 17 |