Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
546 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 142 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 |
|---|---|---|
| 151. C73 | #9643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625863 | 2 |
| #22625646 | 2 |
| C2×#17989437 | 2 |
| C2×Q8⋊#10596833 | 2 |
| #22612500 | 2 |
| #9643 | 73 |