Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
650 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #22611585 | C2 | semidirect |
| 5. #22608061 | C2 | semidirect |
| 6. #22608053 | C2 | semidirect |
| 7. C73×#2135 | C2 | semidirect |
| 9. C2×#14556622 | C4 | semidirect |
| 10. C22×#11924015 | C4 | semidirect |
| 18. #17988591 | C4 | semidirect |
| 19. #17988581 | C4 | semidirect |
| 251. #2135 | D73 | semidirect |
| 256. C73 | #13097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619206 | 2 |
| #22618408 | 2 |
| #22611585 | 2 |
| #22609902 | 2 |
| #22608061 | 2 |
| #22608053 | 2 |
| C73×#2135 | 2 |
| #13097 | 73 |