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. #22625689 | C2 | semidirect |
| 4. #22625030 | C2 | semidirect |
| 6. C2×#14556679 | C4 | semidirect |
| 10. #17989591 | C4 | semidirect |
| 12. #17989562 | C4 | semidirect |
| 15. #17989546 | C4 | semidirect |
| 16. #17989497 | C4 | semidirect |
| 17. #17989496 | C4 | semidirect |
| 157. C73 | #12634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626657 | 2 |
| #22626225 | 2 |
| #22625689 | 2 |
| #22625030 | 2 |
| #22611595 | 2 |
| #12634 | 73 |