Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
680 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22607953 | C2 | semidirect |
| 5. C23×Dic146 | C4 | semidirect |
| 9. #17988499 | C4 | semidirect |
| 13. C2×#14556498 | C4 | semidirect |
| 196. C73 | #11808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988499 | 2 |
| #22610005 | 2 |
| #22607953 | 2 |
| C73×#1462 | 2 |
| #11808 | 73 |