Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
356 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 25. #17988334 | C4 | semidirect |
| 26. #17988333 | C4 | semidirect |
| 27. #17988332 | C4 | semidirect |
| 28. #332×C73 | C4 | semidirect |
| 157. C73 | #8936 | semidirect |
| 178. #332 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626842 | 2 |
| #22626116 | 2 |
| #22625509 | 2 |
| #22624758 | 2 |
| #22608594 | 2 |
| #8936 | 73 |