Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
456 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 96 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. #22625687 | C2 | semidirect |
| 3. #22625023 | C2 | semidirect |
| 4. #22625020 | C2 | semidirect |
| 9. #17989489 | C4 | semidirect |
| 10. #17989487 | C4 | semidirect |
| 13. C22×#11924012 | C4 | semidirect |
| 17. #17988615 | C4 | semidirect |
| 19. #17988545 | C4 | semidirect |
| 20. #407×C73 | C4 | semidirect |
| 148. C73 | #12624 | semidirect |
| 158. #407 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626182 | 2 |
| #22625687 | 2 |
| #22625023 | 2 |
| #22625020 | 2 |
| #22618630 | 2 |
| #12624 | 73 |