Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
626 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 164 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 |
|---|---|---|
| 8. #17989456 | C4 | semidirect |
| 135. C73 | #10815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625636 | 2 |
| #22625623 | 2 |
| C2×#17989456 | 2 |
| C2×#17988541 | 2 |
| #10815 | 73 |