Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
342 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 5. #17989686 | C4 | semidirect |
| 129. C73 | #7193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989686 | 2 |
| #22625595 | 2 |
| #7193 | 73 |