Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
668 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 147 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. C2×#11763251 | C2 | semidirect |
| 2. #14540526 | C2 | semidirect |
| 3. #14531045 | C2 | semidirect |
| 4. #14530898 | C2 | semidirect |
| 5. #14530846 | C2 | semidirect |
| 6. #14530719 | C2 | semidirect |
| 7. #14530710 | C2 | semidirect |
| 8. #14530617 | C2 | semidirect |
| 9. C4×C17×Q32 | C2 | semidirect |
| 58. C17×Q32 | D4 | semidirect |
| 152. C4×Q32 | D17 | semidirect |
| 224. Q32 | D68 | semidirect |
| 239. C17 | #33843 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763251 | 2 |
| #14540526 | 2 |
| #14531045 | 2 |
| #14530898 | 2 |
| #14530846 | 2 |
| #14530719 | 2 |
| #14530710 | 2 |
| #14530617 | 2 |
| C4×C17×Q32 | 2 |
| #33843 | 17 |