Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
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×#11924012 | C2 | semidirect |
| 2. #22618880 | C2 | semidirect |
| 3. #22618866 | C2 | semidirect |
| 4. C2×Q8×#10596831 | C2 | semidirect |
| 32. #14556598 | Q8 | direct (N × H) |
| 66. #11924012 | C2×Q8 | semidirect |
| 68. C2×#10596831 | C2×Q8 | semidirect |
| 99. Q8×C73 | #131 | semidirect |
| 138. C73 | Q8×#131 | semidirect |
| 230. Q8 | #14556598 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11924012 | 2 |
| #22618880 | 2 |
| #22618866 | 2 |
| C2×Q8×#10596831 | 2 |
| #22618499 | 2 |
| C4×#14556598 | 2 |
| Q8×#41×C73 | 2 |
| Q8×#131 | 73 |