Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
206 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 47. #11924031 | Q16 | semidirect |
| 105. C73 | #12053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626346 | 2 |
| #22626345 | 2 |
| #22624961 | 2 |
| #22624898 | 2 |
| Q8⋊#11924031 | 2 |
| #22624843 | 2 |
| #22608735 | 2 |
| #12053 | 73 |