Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 2. #22612148 | C2 | semidirect |
| 3. #22612104 | C2 | semidirect |
| 4. #22612009 | C2 | semidirect |
| 6. #22611820 | C2 | semidirect |
| 7. #22611747 | C2 | semidirect |
| 8. C73×#3177 | C2 | semidirect |
| 18. #17988409 | C22 | semidirect |
| 19. #17988408 | C22 | semidirect |
| 20. #17988403 | C22 | semidirect |
| 23. #17988365 | C22 | semidirect |
| 25. #499×C73 | C22 | semidirect |
| 26. #494×C73 | C22 | semidirect |
| 30. #441×C73 | C22 | semidirect |
| 161. #3177 | D73 | semidirect |
| 169. C73 | #33693 | semidirect |
| 174. #499 | C2×D73 | semidirect |
| 175. #494 | C2×D73 | semidirect |
| 183. #441 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618835 | 2 |
| #22612148 | 2 |
| #22612104 | 2 |
| #22612009 | 2 |
| #22611881 | 2 |
| #22611820 | 2 |
| #22611747 | 2 |
| C73×#3177 | 2 |
| #33693 | 73 |