Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
624 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 142 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 |
|---|---|---|
| 18. #17988611 | C4 | semidirect |
| 19. #17988610 | C4 | semidirect |
| 20. #17988610 | C4 | semidirect |
| 21. #423×C73 | C4 | semidirect |
| 178. C73 | #11245 | semidirect |
| 191. #423 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626584 | 2 |
| #22625643 | 2 |
| D73⋊#338 | 2 |
| C2×#17989454 | 2 |
| #22618493 | 2 |
| #11245 | 73 |