Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
788 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 788 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. #22620887 | C2 | semidirect |
| 2. #22620846 | C2 | semidirect |
| 3. #22620306 | C2 | semidirect |
| 4. #22609596 | C2 | semidirect |
| 5. #22609589 | C2 | semidirect |
| 6. #22609567 | C2 | semidirect |
| 7. #22609535 | C2 | semidirect |
| 8. #22608228 | C2 | semidirect |
| 9. C73×#3184 | C2 | semidirect |
| 12. #17988966 | C22 | semidirect |
| 15. #17988959 | C22 | semidirect |
| 17. #17988937 | C22 | semidirect |
| 22. #17988933 | C22 | semidirect |
| 29. #17988309 | C22 | semidirect |
| 30. #17988308 | C22 | semidirect |
| 31. C8×#10596831 | C22 | semidirect |
| 33. #498×C73 | C22 | semidirect |
| 34. #493×C73 | C22 | semidirect |
| 35. #486×C73 | C22 | semidirect |
| 172. #3184 | D73 | semidirect |
| 179. C73 | #19729 | semidirect |
| 183. #498 | C2×D73 | semidirect |
| 187. #493 | C2×D73 | semidirect |
| 196. #486 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620887 | 2 |
| #22620846 | 2 |
| #22620306 | 2 |
| #22609596 | 2 |
| #22609589 | 2 |
| #22609567 | 2 |
| #22609535 | 2 |
| #22608228 | 2 |
| C73×#3184 | 2 |
| #19729 | 73 |