Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
462 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 462 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. #11763722 | C4 | semidirect |
| 15. C4×Dic68 | C4 | semidirect |
| 16. Q16×Dic17 | C4 | semidirect |
| 17. #11762903 | C4 | semidirect |
| 23. C4×Q16×C17 | C4 | semidirect |
| 76. Q16×C17 | C42 | semidirect |
| 98. Dic68 | C42 | semidirect |
| 166. C4×Q16 | #595 | semidirect |
| 218. C17 | #12638 | semidirect |
| 234. Q16 | C4×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763722 | 2 |
| #14544985 | 2 |
| C4×#10587534 | 2 |
| #14543841 | 2 |
| C4×Q16×D17 | 2 |
| #12638 | 17 |