Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
452 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 452 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 |
|---|---|---|
| 3. #22625687 | C2 | semidirect |
| 4. #22625032 | C2 | semidirect |
| 9. #17989498 | C4 | semidirect |
| 10. #17989496 | C4 | semidirect |
| 14. C2×#14556599 | C4 | semidirect |
| 19. #17988555 | C4 | semidirect |
| 21. C2×#14556502 | C4 | semidirect |
| 22. #423×C73 | C4 | semidirect |
| 152. C73 | #12634 | semidirect |
| 158. #423 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626224 | 2 |
| #22626204 | 2 |
| #22625687 | 2 |
| #22625032 | 2 |
| #22618648 | 2 |
| #12634 | 73 |