Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
452 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 92 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. #22625690 | C2 | semidirect |
| 4. #22625033 | C2 | semidirect |
| 6. C2×#14556679 | C4 | semidirect |
| 10. #17989592 | C4 | semidirect |
| 12. #17989562 | C4 | semidirect |
| 15. #17989546 | C4 | semidirect |
| 21. #17988386 | C4 | semidirect |
| 22. #17988383 | C4 | semidirect |
| 23. #356×C73 | C4 | semidirect |
| 156. C73 | #12634 | semidirect |
| 170. #356 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626658 | 2 |
| #22626205 | 2 |
| #22625690 | 2 |
| #22625033 | 2 |
| #22611615 | 2 |
| #12634 | 73 |