Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
212 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 49. #11924018 | C16 | semidirect |
| 105. C73 | #12059 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626345 | 2 |
| Q8×#11924031 | 2 |
| #22624954 | 2 |
| #22624898 | 2 |
| Q8⋊#11924031 | 2 |
| #22624846 | 2 |
| #22608735 | 2 |
| #12059 | 73 |