Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
644 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 107 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. #14528772 | C2 | semidirect |
| 2. #14527102 | C2 | semidirect |
| 3. #14526781 | C2 | semidirect |
| 12. C2×C17×#127 | C4 | semidirect |
| 16. C17×#392 | C4 | semidirect |
| 19. C4×C4⋊C4×C17 | C4 | semidirect |
| 191. C2×#127 | Dic17 | semidirect |
| 197. #392 | Dic17 | semidirect |
| 201. C4×C4⋊C4 | Dic17 | semidirect |
| 246. C17 | #11877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14528772 | 2 |
| #14527102 | 2 |
| #14526781 | 2 |
| C17×#2541 | 2 |
| #11877 | 17 |