Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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. #14531096 | C2 | semidirect |
| 2. #14531032 | C2 | semidirect |
| 3. #14530665 | C2 | semidirect |
| 4. #14526981 | C2 | semidirect |
| 5. #14526975 | C2 | semidirect |
| 6. #14526974 | C2 | semidirect |
| 7. C17×#2263 | C2 | semidirect |
| 29. C17×Q32 | D4 | semidirect |
| 33. C17×D16 | D4 | semidirect |
| 86. #2263 | D17 | semidirect |
| 128. Q32 | C22⋊D17 | semidirect |
| 135. D16 | C22⋊D17 | semidirect |
| 143. C17 | #13692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14531096 | 2 |
| #14531032 | 2 |
| #14530665 | 2 |
| #14526981 | 2 |
| #14526975 | 2 |
| #14526974 | 2 |
| C17×#2263 | 2 |
| #13692 | 17 |