Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
472 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 2. #22625835 | C2 | semidirect |
| 3. #22625831 | C2 | semidirect |
| 5. #22624833 | C2 | semidirect |
| 6. #22624802 | C2 | semidirect |
| 27. #17988915 | C4 | semidirect |
| 29. #17988901 | C4 | semidirect |
| 30. #17988900 | C4 | semidirect |
| 34. #483×C73 | C4 | semidirect |
| 238. C73 | #9521 | semidirect |
| 243. #483 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626802 | 2 |
| #22625835 | 2 |
| #22625831 | 2 |
| #22625349 | 2 |
| #22624833 | 2 |
| #22624802 | 2 |
| #22619855 | 2 |
| #9521 | 73 |