Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1168 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 139 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. C2×#11762596 | C2 | semidirect |
| 2. #14528712 | C2 | semidirect |
| 3. #14528702 | C2 | semidirect |
| 13. C23×D4×C17 | C4 | semidirect |
| 19. C2×C17×#120 | C4 | semidirect |
| 21. C2×C17×#117 | C4 | semidirect |
| 208. C23×D4 | Dic17 | semidirect |
| 214. C2×#120 | Dic17 | semidirect |
| 216. C2×#117 | Dic17 | semidirect |
| 272. C17 | #12691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11762596 | 2 |
| #14528712 | 2 |
| #14528702 | 2 |
| C2×C17×#535 | 2 |
| #12691 | 17 |