Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
466 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 466 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. C2×#17989019 | C2 | semidirect |
| 2. #22612251 | C2 | semidirect |
| 3. #22612246 | C2 | semidirect |
| 4. #22612240 | C2 | semidirect |
| 5. C2×M64×C73 | C2 | semidirect |
| 10. #17989019 | C22 | semidirect |
| 11. C2×Dic584 | C22 | semidirect |
| 13. C2×D1168 | C22 | semidirect |
| 14. Dic1168 | C22 | semidirect |
| 15. #17988426 | C22 | semidirect |
| 16. D2336 | C22 | semidirect |
| 18. M64×C73 | C22 | semidirect |
| 19. C2×C32×C73 | C22 | semidirect |
| 98. C2×M64 | D73 | semidirect |
| 99. C73 | #33981 | semidirect |
| 112. M64 | C2×D73 | semidirect |
| 113. C2×C32 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989019 | 2 |
| #22612251 | 2 |
| #22612246 | 2 |
| #22612240 | 2 |
| C2×M64×C73 | 2 |
| #33981 | 73 |