Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#22583641 | C2 | semidirect |
| 3. C22×#17985382 | C2 | semidirect |
| 4. #31826625 | C2 | semidirect |
| 5. #31826620 | C2 | semidirect |
| 6. #31826473 | C2 | semidirect |
| 7. #31826459 | C2 | semidirect |
| 8. #31826432 | C2 | semidirect |
| 9. #536×C283 | C2 | semidirect |
| 140. C283 | #3011 | semidirect |
| 145. #536 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583657 | 2 |
| C2×#22583641 | 2 |
| C22×#17985382 | 2 |
| #31826625 | 2 |
| #31826620 | 2 |
| #31826473 | 2 |
| #31826459 | 2 |
| #31826432 | 2 |
| #536×C283 | 2 |
| #3011 | 283 |