Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
292 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 292 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 |
|---|---|---|
| 14. #17989512 | C4 | semidirect |
| 15. #17989511 | C4 | semidirect |
| 16. #17989478 | C4 | semidirect |
| 17. #17989478 | C4 | semidirect |
| 23. #17988417 | C4 | semidirect |
| 24. #17988416 | C4 | semidirect |
| 25. #17988416 | C4 | semidirect |
| 26. #368×C73 | C4 | semidirect |
| 133. C73 | #12678 | semidirect |
| 146. #368 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626278 | 2 |
| C2×#17989478 | 2 |
| #22625752 | 2 |
| #22625740 | 2 |
| #22625011 | 2 |
| #22625008 | 2 |
| #22611724 | 2 |
| #12678 | 73 |