Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1882 conjugacy classes of subgroups.
The subgroup lattice has 262 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×#63223 | C2 | semidirect |
| 2. #14537733 | C2 | semidirect |
| 3. #14537719 | C2 | semidirect |
| 4. C2×Q8×#3622 | C2 | semidirect |
| 51. #10587634 | Q8 | direct (N × H) |
| 88. #63223 | C2×Q8 | semidirect |
| 90. C2×#3622 | C2×Q8 | semidirect |
| 100. Q8×C17 | #131 | semidirect |
| 195. C17 | Q8×#131 | semidirect |
| 230. Q8 | #10587634 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#63223 | 2 |
| #14537733 | 2 |
| #14537719 | 2 |
| C2×Q8×#3622 | 2 |
| #14537352 | 2 |
| C4×#10587634 | 2 |
| Q8×#41×C17 | 2 |
| Q8×#131 | 17 |