Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
368 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 145 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. #31826868 | C2 | semidirect |
| 3. #31826844 | C2 | semidirect |
| 4. #31826817 | C2 | semidirect |
| 5. #31826815 | C2 | semidirect |
| 7. C4×#17985382 | C2 | semidirect |
| 79. C2×C4×C283 | Q16 | semidirect |
| 104. C283 | #3170 | semidirect |
| 182. C2×C4 | #17985382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827022 | 2 |
| #31826868 | 2 |
| #31826844 | 2 |
| #31826817 | 2 |
| #31826815 | 2 |
| #31826704 | 2 |
| C4×#17985382 | 2 |
| C2×C4×C283⋊C8 | 2 |
| #533×C283 | 2 |
| #3170 | 283 |