Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1050 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 176 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 |
|---|---|---|
| 11. C2×#14556590 | C4 | semidirect |
| 12. C2×#14556583 | C4 | semidirect |
| 17. C2×#125×C73 | C4 | semidirect |
| 22. C2×#11924038 | Q8 | semidirect |
| 27. C2×C4×#64408 | Q8 | semidirect |
| 163. C73 | #11386 | semidirect |
| 168. C2×#125 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989457 | 2 |
| #22625595 | 2 |
| C4×(C2×#64408)⋊C4 | 2 |
| C2×#17989143 | 2 |
| #11386 | 73 |