Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
406 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 8. #17989638 | C4 | semidirect |
| 11. Q8×#10596833 | C4 | semidirect |
| 26. #17988336 | C4 | semidirect |
| 27. #17988334 | C4 | semidirect |
| 28. #17988332 | C4 | semidirect |
| 29. #333×C73 | C4 | semidirect |
| 169. C73 | #8258 | semidirect |
| 186. #333 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626720 | 2 |
| #22625724 | 2 |
| #22625315 | 2 |
| #22625147 | 2 |
| #22624828 | 2 |
| #22624823 | 2 |
| #22608585 | 2 |
| #8258 | 73 |