Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
382 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 2. #22626150 | C2 | semidirect |
| 4. #22624984 | C2 | semidirect |
| 10. #17989484 | C4 | semidirect |
| 11. #17989483 | C4 | semidirect |
| 18. C2×#14556531 | C4 | semidirect |
| 19. C2×#14556530 | C4 | semidirect |
| 21. C2×C16×D73 | C4 | semidirect |
| 23. C22×C16×C73 | C4 | semidirect |
| 139. C73 | #12617 | semidirect |
| 149. C22×C16 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626168 | 2 |
| #22626150 | 2 |
| #22625686 | 2 |
| #22624984 | 2 |
| C2×#17989003 | 2 |
| #12617 | 73 |