Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
810 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 176 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. #22626660 | C2 | semidirect |
| 2. #22626658 | C2 | semidirect |
| 3. #22626069 | C2 | semidirect |
| 4. #22626067 | C2 | semidirect |
| 5. #22625923 | C2 | semidirect |
| 6. #22625920 | C2 | semidirect |
| 7. #22625856 | C2 | semidirect |
| 8. #22625649 | C2 | semidirect |
| 28. #17988968 | C4 | semidirect |
| 29. #17988966 | C4 | semidirect |
| 30. #17988963 | C4 | semidirect |
| 31. #17988960 | C4 | semidirect |
| 33. #492×C73 | C4 | semidirect |
| 184. C73 | #22282 | semidirect |
| 194. #492 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626660 | 2 |
| #22626658 | 2 |
| #22626069 | 2 |
| #22626067 | 2 |
| #22625923 | 2 |
| #22625920 | 2 |
| #22625856 | 2 |
| #22625649 | 2 |
| #22620354 | 2 |
| #22282 | 73 |