Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
2302 conjugacy classes of subgroups; only the 832 normal subgroups are shown.
This group has 2302 conjugacy classes of subgroups — too many to draw. Only its 832 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 |
|---|---|---|
| 8. #17989523 | C4 | semidirect |
| 10. C42×#64408 | C4 | semidirect |
| 12. #17988433 | C4 | semidirect |
| 13. #17988432 | C4 | semidirect |
| 15. #376×C73 | C4 | semidirect |
| 40. C4×#64408 | C42 | semidirect |
| 49. C4×Dic73 | C42 | semidirect |
| 50. C4×Dic73 | C42 | semidirect |
| 53. C42×C73 | C42 | semidirect |
| 80. #64408 | #376 | direct (N × H) |
| 94. C73 | C4×#376 | semidirect |
| 102. #376 | #64408 | direct (N × H) |
| 143. C42 | C4×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989523 | 2 |
| C2×C42×#64408 | 2 |
| #95×#64408 | 2 |
| #376×D73 | 2 |
| C4×#376 | 73 |