Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
306 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 19. #17988989 | C4 | semidirect |
| 20. #17988987 | C4 | semidirect |
| 21. #17988984 | C4 | semidirect |
| 26. #498×C73 | C4 | semidirect |
| 30. #14556666 | Q8 | semidirect |
| 34. #14556664 | Q8 | semidirect |
| 156. C73 | #13291 | semidirect |
| 165. #498 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626153 | 2 |
| #22625850 | 2 |
| #22625013 | 2 |
| #22625004 | 2 |
| #22624998 | 2 |
| #22624995 | 2 |
| #22620456 | 2 |
| #13291 | 73 |