Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
684 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 24. C22×Dic146 | Q8 | semidirect |
| 209. C73 | #10341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22609865 | 2 |
| #22608201 | 2 |
| #22607809 | 2 |
| #22607774 | 2 |
| C73×#2659 | 2 |
| #10341 | 73 |