Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1148 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 224 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. #22626777 | C2 | semidirect |
| 2. #22625419 | C2 | semidirect |
| 3. #22625390 | C2 | semidirect |
| 4. #22625385 | C2 | semidirect |
| 8. #17989608 | C22 | semidirect |
| 9. C4×#11924037 | C22 | semidirect |
| 10. #17989443 | C22 | semidirect |
| 11. #17989443 | C22 | semidirect |
| 12. #17989442 | C22 | semidirect |
| 13. #17989442 | C22 | semidirect |
| 149. C73 | #17688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626777 | 2 |
| #22625419 | 2 |
| #22625390 | 2 |
| #22625385 | 2 |
| #22623719 | 2 |
| #17688 | 73 |