Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
334 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 3. Q8⋊#11924031 | C2 | semidirect |
| 117. C73 | #11608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626263 | 2 |
| C2×C4×#11924031 | 2 |
| Q8⋊#11924031 | 2 |
| #22618866 | 2 |
| #11608 | 73 |