Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
820 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 152 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 |
|---|---|---|
| 20. C2×#11924037 | Q8 | semidirect |
| 22. C22×#10596833 | Q8 | semidirect |
| 115. C73 | #11395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989468 | 2 |
| #22623333 | 2 |
| #11395 | 73 |