Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1206 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1206 conjugacy classes of subgroups — too many to draw. Only its 147 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×#11762604 | C2 | semidirect |
| 8. C23×Q8×C17 | C4 | semidirect |
| 12. C2×C17×#124 | C4 | semidirect |
| 15. C22×C42×C17 | C4 | semidirect |
| 60. C2×Q8×C17 | C22⋊C4 | semidirect |
| 88. C42×C17 | C22⋊C4 | semidirect |
| 150. C22×C17 | #354 | semidirect |
| 159. C23×Q8 | Dic17 | semidirect |
| 163. C2×#124 | Dic17 | semidirect |
| 166. C22×C42 | Dic17 | semidirect |
| 208. C17 | #12694 | semidirect |
| 223. C2×Q8 | C22⋊Dic17 | semidirect |
| 254. C42 | C22⋊Dic17 | semidirect |
| 309. C22 | #11762604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11762604 | 2 |
| #14528699 | 2 |
| C22×C17×#124 | 2 |
| #12694 | 17 |