Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
390 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 148 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. #17989451 | C4 | semidirect |
| 12. #17989448 | C4 | semidirect |
| 17. #17988340 | C4 | semidirect |
| 18. #17988337 | C4 | semidirect |
| 19. #335×C73 | C4 | semidirect |
| 27. #14556645 | C8 | semidirect |
| 113. C73 | #8268 | semidirect |
| 123. #335 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556645 | 2 |
| #22625479 | 2 |
| #22625137 | 2 |
| #22624758 | 2 |
| #22608678 | 2 |
| #8268 | 73 |