Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
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×#6099 | C2 | semidirect |
| 2. #13123785 | C2 | semidirect |
| 3. #13123771 | C2 | semidirect |
| 4. C2×Q8×#1055 | C2 | semidirect |
| 51. #88202 | Q8 | direct (N × H) |
| 89. #6099 | C2×Q8 | semidirect |
| 91. C2×#1055 | C2×Q8 | semidirect |
| 107. Q8×C13 | #131 | semidirect |
| 225. C13 | Q8×#131 | semidirect |
| 230. Q8 | #88202 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#6099 | 2 |
| #13123785 | 2 |
| #13123771 | 2 |
| C2×Q8×#1055 | 2 |
| #13123404 | 2 |
| C4×#88202 | 2 |
| Q8×C13×#41 | 2 |
| Q8×#131 | 13 |