Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
664 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 25. C22⋊#10596833 | Q8 | semidirect |
| 174. C73 | #9882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625787 | 2 |
| #22625657 | 2 |
| #22624769 | 2 |
| C2×#17988494 | 2 |
| #9882 | 73 |