Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
240 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 9. #17989428 | C4 | semidirect |
| 13. #17988408 | C4 | semidirect |
| 15. #364×C73 | C4 | semidirect |
| 19. #14556661 | C8 | semidirect |
| 21. #14556659 | C8 | semidirect |
| 104. C73 | #7181 | semidirect |
| 113. #364 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625733 | 2 |
| #22625135 | 2 |
| #364×D73 | 2 |
| #7181 | 73 |