Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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×#22583632 | C2 | semidirect |
| 2. C2×#22583630 | C2 | semidirect |
| 3. #31827011 | C2 | semidirect |
| 4. #31826858 | C2 | semidirect |
| 5. #31826856 | C2 | semidirect |
| 6. #31826853 | C2 | semidirect |
| 7. #31826851 | C2 | semidirect |
| 8. C2×#22583520 | C2 | semidirect |
| 9. C2×#135×C283 | C2 | semidirect |
| 51. C2×C283⋊C8 | D4 | semidirect |
| 68. C2×C8×C283 | D4 | semidirect |
| 116. C283 | #3150 | semidirect |
| 120. C2×#135 | D283 | semidirect |
| 180. C2×C8 | C22⋊D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583632 | 2 |
| C2×#22583630 | 2 |
| #31827011 | 2 |
| #31826858 | 2 |
| #31826856 | 2 |
| #31826853 | 2 |
| #31826851 | 2 |
| C2×#22583520 | 2 |
| C2×#135×C283 | 2 |
| #3150 | 283 |