Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
354 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 74 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. D73⋊#365 | C2 | semidirect |
| 4. #22625752 | C2 | semidirect |
| 5. #22624997 | C2 | semidirect |
| 6. #22624977 | C2 | semidirect |
| 23. #17988401 | C4 | semidirect |
| 24. #17988400 | C4 | semidirect |
| 25. #17988399 | C4 | semidirect |
| 26. #361×C73 | C4 | semidirect |
| 167. C73 | #13138 | semidirect |
| 185. #361 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D73⋊#365 | 2 |
| D73⋊#361 | 2 |
| #22626080 | 2 |
| #22625752 | 2 |
| #22624997 | 2 |
| #22624977 | 2 |
| #361×D73 | 2 |
| #13138 | 73 |