Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
446 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 106 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. #14545117 | C2 | semidirect |
| 3. #14544719 | C2 | semidirect |
| 4. #14543855 | C2 | semidirect |
| 15. Q16×Dic17 | C4 | semidirect |
| 18. C4×D136 | C4 | semidirect |
| 19. #11762891 | C4 | semidirect |
| 23. C4×Q16×C17 | C4 | semidirect |
| 83. Q16×C17 | C4⋊C4 | semidirect |
| 105. D136 | C4⋊C4 | semidirect |
| 167. C4×C17 | #360 | semidirect |
| 172. Dic17 | #360 | semidirect |
| 179. C4×Q16 | #595 | semidirect |
| 239. C17 | #12816 | semidirect |
| 255. Q16 | C4⋊#595 | semidirect |
| 342. C4 | #11763726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545117 | 2 |
| C2×#11763726 | 2 |
| #14544719 | 2 |
| #14543855 | 2 |
| C4×#10587605 | 2 |
| #12816 | 17 |