Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
418 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 73 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. #14531008 | C2 | semidirect |
| 3. #14530932 | C2 | semidirect |
| 4. #14528183 | C2 | semidirect |
| 5. #14526831 | C2 | semidirect |
| 6. #14526746 | C2 | semidirect |
| 7. C17×D4⋊C16 | C2 | semidirect |
| 10. #11763214 | C22 | semidirect |
| 20. #11762562 | C22 | semidirect |
| 23. C17×C4⋊C16 | C22 | semidirect |
| 24. C4×C16×C17 | C22 | semidirect |
| 131. D4⋊C16 | D17 | semidirect |
| 162. C4⋊C16 | C2×D17 | semidirect |
| 165. C4×C16 | C2×D17 | semidirect |
| 203. C17 | #12372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D136 | 2 |
| #14531008 | 2 |
| #14530932 | 2 |
| #14528183 | 2 |
| #14526831 | 2 |
| #14526746 | 2 |
| C17×D4⋊C16 | 2 |
| #12372 | 17 |