Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
476 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22608352 | C2 | semidirect |
| 5. #22607820 | C2 | semidirect |
| 6. #22607764 | C2 | semidirect |
| 7. C73×#1994 | C2 | semidirect |
| 10. #17988869 | C4 | semidirect |
| 11. #17988864 | C4 | semidirect |
| 12. #17988794 | C4 | semidirect |
| 13. #17988789 | C4 | semidirect |
| 208. #1994 | D73 | semidirect |
| 213. C73 | #8972 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619996 | 2 |
| #22619061 | 2 |
| C4×#14556519 | 2 |
| #22608352 | 2 |
| #22607820 | 2 |
| #22607764 | 2 |
| C73×#1994 | 2 |
| #8972 | 73 |