Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
358 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 358 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 |
|---|---|---|
| 9. #11763736 | C4 | semidirect |
| 10. #11763735 | C4 | semidirect |
| 15. #11762585 | C4 | semidirect |
| 16. #11762584 | C4 | semidirect |
| 17. #11762584 | C4 | semidirect |
| 18. C17×#346 | C4 | semidirect |
| 65. C16×C17 | C42 | semidirect |
| 67. #63214 | C42 | semidirect |
| 121. #346 | #595 | semidirect |
| 151. C17 | #12674 | semidirect |
| 177. C16 | C4×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763736 | 2 |
| C2×#11763735 | 2 |
| C4×#10587534 | 2 |
| #14543842 | 2 |
| D17×#346 | 2 |
| #12674 | 17 |