Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
730 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 7. C2×C22⋊#10596833 | C4 | semidirect |
| 11. C2×C22⋊#10596831 | C4 | semidirect |
| 14. C2×C22⋊C8×C73 | C4 | semidirect |
| 20. C2×C22⋊#64408 | C8 | semidirect |
| 232. C73 | #7032 | semidirect |
| 241. C2×C22⋊C8 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625754 | 2 |
| #22625105 | 2 |
| #22609840 | 2 |
| #7032 | 73 |