Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
334 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 106 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. #22624898 | C2 | semidirect |
| 4. Q8⋊#11924031 | C2 | semidirect |
| 141. C73 | #11608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626264 | 2 |
| C4×#14556664 | 2 |
| #22624898 | 2 |
| Q8⋊#11924031 | 2 |
| #22618862 | 2 |
| #11608 | 73 |