Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22620590 | C2 | semidirect |
| 3. #22612151 | C2 | semidirect |
| 4. #22612108 | C2 | semidirect |
| 5. #22612013 | C2 | semidirect |
| 7. #22611824 | C2 | semidirect |
| 8. C73×#2166 | C2 | semidirect |
| 13. #17988989 | C22 | semidirect |
| 14. #17988967 | C22 | semidirect |
| 22. #17988695 | C22 | semidirect |
| 26. #17988410 | C22 | semidirect |
| 27. #17988404 | C22 | semidirect |
| 30. #364×C73 | C22 | semidirect |
| 32. #347×C73 | C22 | semidirect |
| 168. #2166 | D73 | semidirect |
| 169. C73 | #33693 | semidirect |
| 189. #364 | C2×D73 | semidirect |
| 193. #347 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620590 | 2 |
| #22618835 | 2 |
| #22612151 | 2 |
| #22612108 | 2 |
| #22612013 | 2 |
| #22611884 | 2 |
| #22611824 | 2 |
| C73×#2166 | 2 |
| #33693 | 73 |