Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
996 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 996 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. #22624331 | C2 | semidirect |
| 2. #22620849 | C2 | semidirect |
| 3. #22609017 | C2 | semidirect |
| 4. #22608596 | C2 | semidirect |
| 5. #22608349 | C2 | semidirect |
| 6. C73×#3138 | C2 | semidirect |
| 10. #17989240 | C22 | semidirect |
| 19. #17988333 | C22 | semidirect |
| 20. #17988316 | C22 | semidirect |
| 155. #3138 | D73 | semidirect |
| 159. C73 | #18727 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22624331 | 2 |
| #22620849 | 2 |
| #22609017 | 2 |
| #22608596 | 2 |
| #22608349 | 2 |
| C73×#3138 | 2 |
| #18727 | 73 |