Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
424 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 81. C2×#10596831 | Q16 | semidirect |
| 174. C73 | #9048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619970 | 2 |
| #22618868 | 2 |
| #22610872 | 2 |
| #22608586 | 2 |
| #22607826 | 2 |
| #22607775 | 2 |
| C73×#1487 | 2 |
| #9048 | 73 |