Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
190 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 6. #17989518 | C4 | semidirect |
| 9. #17989513 | C4 | semidirect |
| 12. #17988413 | C4 | semidirect |
| 14. #366×C73 | C4 | semidirect |
| 91. C73 | #7471 | semidirect |
| 102. #366 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989518 | 2 |
| C2×#17989513 | 2 |
| #366×D73 | 2 |
| #7471 | 73 |