Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
734 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 734 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 1. C2×#17989430 | C2 | semidirect |
| 2. #22624857 | C2 | semidirect |
| 3. #22624855 | C2 | semidirect |
| 41. C22×D4×C73 | C8 | semidirect |
| 73. C24×C73 | C2×C8 | semidirect |
| 88. C22×C4×C73 | C2×C8 | semidirect |
| 187. C73 | #11426 | semidirect |
| 207. C22×D4 | #10596833 | semidirect |
| 237. C24 | C2×#10596833 | semidirect |
| 261. C22×C4 | C2×#10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989430 | 2 |
| #22624857 | 2 |
| #22624855 | 2 |
| #22612509 | 2 |
| #11426 | 73 |