Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1774 conjugacy classes of subgroups; only the 432 normal subgroups are shown.
This group has 1774 conjugacy classes of subgroups — too many to draw. Only its 432 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 |
|---|---|---|
| 9. #17988433 | C4 | semidirect |
| 10. #17988432 | C4 | semidirect |
| 12. #376×C73 | C4 | semidirect |
| 40. C4×Dic73 | C4⋊C4 | semidirect |
| 41. C4×Dic73 | C4⋊C4 | semidirect |
| 44. C42×C73 | C4⋊C4 | semidirect |
| 81. C73 | #13856 | semidirect |
| 88. #376 | #64408 | semidirect |
| 122. C42 | C4⋊#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C4⋊#64408 | 2 |
| #22625119 | 2 |
| #376×D73 | 2 |
| #13856 | 73 |