Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1974 conjugacy classes of subgroups.
The subgroup lattice has 314 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14537873 | C2 | semidirect |
| 2. #14537869 | C2 | semidirect |
| 3. #14537865 | C2 | semidirect |
| 4. Q8×#63223 | C2 | semidirect |
| 7. #11762940 | C22 | semidirect |
| 8. Q8×#3622 | C22 | semidirect |
| 67. C2×Q8×C17 | M16 | semidirect |
| 219. C17 | #60248 | semidirect |
| 224. C2×Q8 | #63223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14537873 | 2 |
| #14537869 | 2 |
| #14537865 | 2 |
| Q8×#63223 | 2 |
| #14537417 | 2 |
| C22×C4×Q8×C17 | 2 |
| #60248 | 17 |