Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
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×#11719917 | C2 | semidirect |
| 2. #20283664 | C2 | semidirect |
| 3. #20283650 | C2 | semidirect |
| 4. C2×Q8×#88322 | C2 | semidirect |
| 32. #13133224 | Q8 | direct (N × H) |
| 88. #11719917 | C2×Q8 | semidirect |
| 90. C2×#88322 | C2×Q8 | semidirect |
| 99. Q8×C53 | #131 | semidirect |
| 161. C53 | Q8×#131 | semidirect |
| 230. Q8 | #13133224 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11719917 | 2 |
| #20283664 | 2 |
| #20283650 | 2 |
| C2×Q8×#88322 | 2 |
| #20283283 | 2 |
| C4×#13133224 | 2 |
| Q8×#41×C53 | 2 |
| Q8×#131 | 53 |