Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
222 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 4. C2×#22583520 | C2 | semidirect |
| 5. #31826229 | C2 | semidirect |
| 6. #31826224 | C2 | semidirect |
| 7. #424×C283 | C2 | semidirect |
| 13. #22583533 | C4 | semidirect |
| 14. #22583530 | C4 | semidirect |
| 90. C283 | #1938 | semidirect |
| 92. #424 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583536 | 2 |
| #31826459 | 2 |
| #31826431 | 2 |
| C2×#22583520 | 2 |
| #31826229 | 2 |
| #31826224 | 2 |
| #424×C283 | 2 |
| #1938 | 283 |