Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
606 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 606 conjugacy classes of subgroups — too many to draw. Only its 143 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. #14540659 | C2 | semidirect |
| 3. #14528287 | C2 | semidirect |
| 4. #14528232 | C2 | semidirect |
| 5. #14528030 | C2 | semidirect |
| 6. #14527915 | C2 | semidirect |
| 7. #14527682 | C2 | semidirect |
| 9. C17×#1707 | C2 | semidirect |
| 117. D136 | Q16 | semidirect |
| 150. #1707 | D17 | semidirect |
| 247. C17 | #19927 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14541688 | 2 |
| #14540659 | 2 |
| #14528287 | 2 |
| #14528232 | 2 |
| #14528030 | 2 |
| #14527915 | 2 |
| #14527682 | 2 |
| C8×D136 | 2 |
| C17×#1707 | 2 |
| #19927 | 17 |