Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
574 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 1. #22626371 | C2 | semidirect |
| 4. #22625274 | C2 | semidirect |
| 5. #22624818 | C2 | semidirect |
| 6. #22624783 | C2 | semidirect |
| 25. #17988879 | C4 | semidirect |
| 26. #17988788 | C4 | semidirect |
| 27. #17988787 | C4 | semidirect |
| 32. #477×C73 | C4 | semidirect |
| 153. Q8×C73 | #104 | semidirect |
| 182. Dic146 | #104 | semidirect |
| 224. C73 | #9326 | semidirect |
| 230. #477 | #64408 | semidirect |
| 364. Q8 | #14556656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626371 | 2 |
| #22626094 | 2 |
| #22625322 | 2 |
| #22625274 | 2 |
| #22624818 | 2 |
| #22624783 | 2 |
| #22620055 | 2 |
| #9326 | 73 |