Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
322 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 17. C22×#10596831 | C8 | semidirect |
| 28. C2×M16×C73 | C8 | semidirect |
| 121. C73 | #7188 | semidirect |
| 133. C2×M16 | #10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625162 | 2 |
| #22609629 | 2 |
| #7188 | 73 |