Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
508 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 1. #22626160 | C2 | semidirect |
| 2. #22625617 | C2 | semidirect |
| 3. #22624917 | C2 | semidirect |
| 8. #17989482 | C22 | semidirect |
| 10. #17989461 | C22 | semidirect |
| 15. #17988820 | C4 | semidirect |
| 17. C2×#14556525 | C4 | semidirect |
| 19. C22×D8×C73 | C4 | semidirect |
| 161. C73 | #11705 | semidirect |
| 162. C22×D8 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626160 | 2 |
| #22625617 | 2 |
| #22624917 | 2 |
| C2×#17988820 | 2 |
| #11705 | 73 |