Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 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 |
|---|---|---|
| 1. C2×#22583643 | C2 | semidirect |
| 3. C22×#17985382 | C2 | semidirect |
| 4. #31827039 | C2 | semidirect |
| 5. #31827036 | C2 | semidirect |
| 6. #31826858 | C2 | semidirect |
| 7. #31826856 | C2 | semidirect |
| 8. #31826846 | C2 | semidirect |
| 9. #31826843 | C2 | semidirect |
| 10. #31826423 | C2 | semidirect |
| 11. C2×#137×C283 | C2 | semidirect |
| 143. C283 | #3156 | semidirect |
| 146. C2×#137 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583643 | 2 |
| C2×#22583630 | 2 |
| C22×#17985382 | 2 |
| #31827039 | 2 |
| #31827036 | 2 |
| #31826858 | 2 |
| #31826856 | 2 |
| #31826846 | 2 |
| #31826843 | 2 |
| #31826423 | 2 |
| C2×#137×C283 | 2 |
| #3156 | 283 |