Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
612 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 5. C23×Dic146 | C4 | semidirect |
| 12. #17988459 | C4 | semidirect |
| 14. #17988447 | C4 | semidirect |
| 49. #100×C73 | Q8 | semidirect |
| 182. C73 | #13293 | semidirect |
| 222. #100 | Dic146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22613296 | 2 |
| #22609919 | 2 |
| #22608050 | 2 |
| C4×#100×C73 | 2 |
| #13293 | 73 |