Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
538 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #14528861 | C2 | semidirect |
| 5. #14526693 | C2 | semidirect |
| 6. #14526637 | C2 | semidirect |
| 7. C17×#1826 | C2 | semidirect |
| 10. #11763127 | C4 | semidirect |
| 11. #11763122 | C4 | semidirect |
| 40. C2×C4⋊C4×C17 | C2×C4 | semidirect |
| 41. C2×C4⋊C4×C17 | C2×C4 | semidirect |
| 72. C22⋊#3622 | C2×C4 | semidirect |
| 194. #1826 | D17 | semidirect |
| 278. C2×C4⋊C4 | C4×D17 | semidirect |
| 279. C2×C4⋊C4 | C4×D17 | semidirect |
| 308. C17 | #9525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14538724 | 2 |
| #14531549 | 2 |
| #14528861 | 2 |
| #14527314 | 2 |
| #14526693 | 2 |
| #14526637 | 2 |
| C17×#1826 | 2 |
| #9525 | 17 |