Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
262 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 262 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 |
|---|---|---|
| 19. #17988414 | C4 | semidirect |
| 20. #17988414 | C4 | semidirect |
| 21. #17988413 | C4 | semidirect |
| 22. #366×C73 | C4 | semidirect |
| 133. C73 | #13113 | semidirect |
| 146. #366 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626039 | 2 |
| #22625735 | 2 |
| #22624992 | 2 |
| #22624991 | 2 |
| #22624968 | 2 |
| #22611712 | 2 |
| #13113 | 73 |