Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
508 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 86 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. #22626422 | C2 | semidirect |
| 3. #22625441 | C2 | semidirect |
| 5. #22624785 | C2 | semidirect |
| 6. #22624754 | C2 | semidirect |
| 22. #17988990 | C4 | semidirect |
| 23. #17988935 | C4 | semidirect |
| 24. #17988934 | C4 | semidirect |
| 28. #500×C73 | C4 | semidirect |
| 210. C73 | #9300 | semidirect |
| 215. #500 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626422 | 2 |
| #22626067 | 2 |
| #22625441 | 2 |
| #22625362 | 2 |
| #22624785 | 2 |
| #22624754 | 2 |
| #22621053 | 2 |
| #9300 | 73 |