Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
306 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 33. #14556527 | C8 | semidirect |
| 118. C73 | #9608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625484 | 2 |
| C2×#17989450 | 2 |
| #22625134 | 2 |
| #22624777 | 2 |
| #108×Dic73 | 2 |
| #9608 | 73 |