Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
464 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 78 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. #22625883 | C2 | semidirect |
| 4. #22625877 | C2 | semidirect |
| 5. #22624812 | C2 | semidirect |
| 6. #22624772 | C2 | semidirect |
| 27. #17988325 | C4 | semidirect |
| 28. #17988323 | C4 | semidirect |
| 29. #17988321 | C4 | semidirect |
| 30. #327×C73 | C4 | semidirect |
| 225. C73 | #8874 | semidirect |
| 248. #327 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626798 | 2 |
| #22625914 | 2 |
| #22625883 | 2 |
| #22625877 | 2 |
| #22624812 | 2 |
| #22624772 | 2 |
| #22608419 | 2 |
| #8874 | 73 |