Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
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. #22619020 | C2 | semidirect |
| 2. #22619016 | C2 | semidirect |
| 3. #22619012 | C2 | semidirect |
| 4. Q8×#11924012 | C2 | semidirect |
| 7. #17988718 | C22 | semidirect |
| 8. Q8×#10596831 | C22 | semidirect |
| 69. C2×Q8×C73 | M16 | semidirect |
| 163. C73 | #60248 | semidirect |
| 224. C2×Q8 | #11924012 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619020 | 2 |
| #22619016 | 2 |
| #22619012 | 2 |
| Q8×#11924012 | 2 |
| #22618564 | 2 |
| C22×C4×Q8×C73 | 2 |
| #60248 | 73 |