Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
554 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 86. Dic292 | Q16 | semidirect |
| 165. C73 | #19931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22622868 | 2 |
| #22622606 | 2 |
| #22609434 | 2 |
| #22609386 | 2 |
| #22609170 | 2 |
| #22609069 | 2 |
| #22608829 | 2 |
| C8×Dic292 | 2 |
| C73×#1707 | 2 |
| #19931 | 73 |