Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
2070 conjugacy classes of subgroups; only the 416 normal subgroups are shown.
This group has 2070 conjugacy classes of subgroups — too many to draw. Only its 416 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 |
|---|---|---|
| 2. #22625119 | C2 | semidirect |
| 9. C2×#14556498 | C4 | semidirect |
| 10. #95×D73 | C4 | semidirect |
| 12. C2×#95×C73 | C4 | semidirect |
| 40. C22×Dic73 | C4⋊C4 | semidirect |
| 46. C2×C4×D73 | C4⋊C4 | semidirect |
| 51. C22×C4×C73 | C4⋊C4 | semidirect |
| 113. C73 | #14353 | semidirect |
| 122. C2×#95 | #64408 | semidirect |
| 159. C22×C4 | C4⋊#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989529 | 2 |
| #22625119 | 2 |
| C2×#95×D73 | 2 |
| #14353 | 73 |