Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
794 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 156 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 |
|---|---|---|
| 12. #17988456 | C4 | semidirect |
| 13. #17988453 | C4 | semidirect |
| 16. #382×C73 | C4 | semidirect |
| 150. C73 | #11359 | semidirect |
| 157. #382 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989457 | 2 |
| #22625595 | 2 |
| C4×(C2×#64408)⋊C4 | 2 |
| #22612337 | 2 |
| #11359 | 73 |