Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
680 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. #14528772 | C2 | semidirect |
| 3. #14526909 | C2 | semidirect |
| 11. C2×C4×D4×C17 | C4 | semidirect |
| 14. C17×#390 | C4 | semidirect |
| 16. C17×#384 | C4 | semidirect |
| 17. C43×C17 | C4 | semidirect |
| 59. C2×D4×C17 | C4⋊C4 | semidirect |
| 90. C42×C17 | C4⋊C4 | semidirect |
| 169. C4×C17 | #353 | semidirect |
| 173. C2×C4×D4 | Dic17 | semidirect |
| 177. #390 | Dic17 | semidirect |
| 179. #384 | Dic17 | semidirect |
| 181. C43 | Dic17 | semidirect |
| 222. C17 | #12797 | semidirect |
| 234. C2×D4 | C4⋊Dic17 | semidirect |
| 268. C42 | C4⋊Dic17 | semidirect |
| 340. C4 | #11762602 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11762602 | 2 |
| #14528772 | 2 |
| #14526909 | 2 |
| C4×C17×#127 | 2 |
| #12797 | 17 |