Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
568 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 27. #17988313 | C4 | semidirect |
| 28. #17988312 | C4 | semidirect |
| 29. #17988312 | C4 | semidirect |
| 30. #324×C73 | C4 | semidirect |
| 274. C73 | #8855 | semidirect |
| 297. #324 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626408 | 2 |
| #22625881 | 2 |
| #22625880 | 2 |
| #22625116 | 2 |
| #22624806 | 2 |
| #324×D73 | 2 |
| #8855 | 73 |