Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
358 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #31826772 | C2 | semidirect |
| 4. #31826675 | C2 | semidirect |
| 6. #31826570 | C2 | semidirect |
| 7. C4×#17985382 | C2 | semidirect |
| 95. C283 | #3127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827077 | 2 |
| #31826806 | 2 |
| #31826772 | 2 |
| #31826675 | 2 |
| #31826621 | 2 |
| #31826570 | 2 |
| C4×#17985382 | 2 |
| #31826526 | 2 |
| #519×C283 | 2 |
| #3127 | 283 |