Finite Group DatabasebetaFinite Group DatabasebetaOrder 18112.
106 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 45 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. #22583618 | C2 | semidirect |
| 3. #22583617 | C2 | semidirect |
| 4. #22583545 | C2 | semidirect |
| 5. #22583538 | C2 | semidirect |
| 6. C4×C283⋊C8 | C2 | semidirect |
| 7. #104×C283 | C2 | semidirect |
| 9. #17985382 | C4 | semidirect |
| 10. #17985380 | C4 | semidirect |
| 11. #17985379 | C4 | semidirect |
| 12. #17985377 | C4 | semidirect |
| 51. C283 | #443 | semidirect |
| 58. #104 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22583630 | 2 |
| #22583618 | 2 |
| #22583617 | 2 |
| #22583545 | 2 |
| #22583538 | 2 |
| C4×C283⋊C8 | 2 |
| #104×C283 | 2 |
| #443 | 283 |