Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
724 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 111 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×#11762602 | C2 | semidirect |
| 2. #14528772 | C2 | semidirect |
| 3. C4×#10587505 | C2 | semidirect |
| 12. C2×C17×#127 | C4 | semidirect |
| 19. C17×#390 | C4 | semidirect |
| 20. C4×C4⋊C4×C17 | C4 | semidirect |
| 52. #10587505 | D4 | semidirect |
| 195. C4×C17 | #353 | semidirect |
| 198. C2×#127 | Dic17 | semidirect |
| 207. #390 | Dic17 | semidirect |
| 209. C4×C4⋊C4 | Dic17 | semidirect |
| 257. C17 | #13223 | semidirect |
| 395. 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 |
| C4×#10587505 | 2 |
| C17×#2541 | 2 |
| #13223 | 17 |