Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
180 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 46 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 |
|---|---|---|
| 7. #17989480 | C4 | semidirect |
| 9. #17989428 | C4 | semidirect |
| 10. C8×#10596833 | C4 | semidirect |
| 82. C73 | #7226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626301 | 2 |
| #22625150 | 2 |
| #22610078 | 2 |
| #7226 | 73 |