Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
564 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 7. #17989493 | C4 | semidirect |
| 10. C2×Q8×Dic73 | C4 | semidirect |
| 15. #17988456 | C4 | semidirect |
| 16. #17988433 | C4 | semidirect |
| 17. #391×C73 | C4 | semidirect |
| 69. C4×Dic73 | C42 | semidirect |
| 73. C2×Q8×C73 | C42 | semidirect |
| 147. C73 | #12627 | semidirect |
| 152. #391 | #64408 | semidirect |
| 191. C2×Q8 | C4×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989493 | 2 |
| #22625676 | 2 |
| #22625025 | 2 |
| #22612645 | 2 |
| #12627 | 73 |