Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1132 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1132 conjugacy classes of subgroups — too many to draw. Only its 163 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. #22624336 | C2 | semidirect |
| 2. #22620849 | C2 | semidirect |
| 3. #22609012 | C2 | semidirect |
| 4. #22608983 | C2 | semidirect |
| 5. #22608593 | C2 | semidirect |
| 6. #22608349 | C2 | semidirect |
| 7. C73×#3151 | C2 | semidirect |
| 9. #17989303 | C22 | semidirect |
| 12. #17989222 | C22 | semidirect |
| 18. #17988779 | C22 | semidirect |
| 20. #17988640 | C22 | semidirect |
| 21. #17988336 | C22 | semidirect |
| 22. #17988331 | C22 | semidirect |
| 23. #17988316 | C22 | semidirect |
| 26. C2×#127×C73 | C22 | semidirect |
| 29. #492×C73 | C22 | semidirect |
| 30. C4×M16×C73 | C22 | semidirect |
| 182. #3151 | D73 | semidirect |
| 187. C73 | #18714 | semidirect |
| 198. C2×#127 | C2×D73 | semidirect |
| 202. #492 | C2×D73 | semidirect |
| 207. C4×M16 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22624336 | 2 |
| #22620849 | 2 |
| #22609012 | 2 |
| #22608983 | 2 |
| #22608593 | 2 |
| #22608349 | 2 |
| C73×#3151 | 2 |
| #18714 | 73 |