Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1306 conjugacy classes of subgroups; only the 279 normal subgroups are shown.
This group has 1306 conjugacy classes of subgroups — too many to draw. Only its 279 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. #22618632 | C2 | semidirect |
| 3. #22610349 | C2 | semidirect |
| 4. #22610217 | C2 | semidirect |
| 5. #22609882 | C2 | semidirect |
| 6. #22609731 | C2 | semidirect |
| 7. C73×#3573 | C2 | semidirect |
| 8. C22×#11924011 | C22 | semidirect |
| 14. #17988615 | C22 | semidirect |
| 18. #17988550 | C22 | semidirect |
| 19. #17988542 | C22 | semidirect |
| 20. #17988358 | C22 | semidirect |
| 57. C2×M16×C73 | D4 | semidirect |
| 60. C22×C8×C73 | D4 | semidirect |
| 145. #3573 | D73 | semidirect |
| 152. C73 | #21484 | semidirect |
| 187. C2×M16 | C22⋊D73 | semidirect |
| 191. C22×C8 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619323 | 2 |
| #22618632 | 2 |
| #22610349 | 2 |
| #22610217 | 2 |
| #22609882 | 2 |
| #22609731 | 2 |
| C73×#3573 | 2 |
| #21484 | 73 |