Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
590 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 151 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. #499×D73 | C2 | semidirect |
| 3. #22612176 | C2 | semidirect |
| 4. #22612174 | C2 | semidirect |
| 5. #22612173 | C2 | semidirect |
| 6. #22612164 | C2 | semidirect |
| 7. #22611642 | C2 | semidirect |
| 8. #22611524 | C2 | semidirect |
| 9. C73×#2245 | C2 | semidirect |
| 152. #2245 | D73 | semidirect |
| 158. C73 | #33708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×D73 | 2 |
| #22620360 | 2 |
| #22612176 | 2 |
| #22612174 | 2 |
| #22612173 | 2 |
| #22612164 | 2 |
| #22611642 | 2 |
| #22611524 | 2 |
| C73×#2245 | 2 |
| #33708 | 73 |