Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
380 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 4. C23×#10596833 | C4 | semidirect |
| 7. C2×C22⋊#10596833 | C4 | semidirect |
| 10. #17989430 | C4 | semidirect |
| 36. #14556506 | C8 | semidirect |
| 41. #99×C73 | C8 | semidirect |
| 173. C73 | #7204 | semidirect |
| 206. #99 | #10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625904 | 2 |
| #22625171 | 2 |
| #99×Dic73 | 2 |
| #7204 | 73 |