Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1974 conjugacy classes of subgroups.
The subgroup lattice has 472 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14545685 | C2 | semidirect |
| 2. #14545683 | C2 | semidirect |
| 3. #14545680 | C2 | semidirect |
| 4. #14545679 | C2 | semidirect |
| 5. #14545586 | C2 | semidirect |
| 9. #11763861 | C22 | semidirect |
| 10. #11763860 | C22 | semidirect |
| 11. #11763858 | C22 | semidirect |
| 134. C2×Dic34 | M16 | semidirect |
| 336. C17 | #60248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545685 | 2 |
| #14545683 | 2 |
| #14545680 | 2 |
| #14545679 | 2 |
| #14545586 | 2 |
| #14545463 | 2 |
| #14545461 | 2 |
| C2×C4×Q8×D17 | 2 |
| #60248 | 17 |