Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 141 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. #31826815 | C2 | semidirect |
| 3. #31826798 | C2 | semidirect |
| 4. #31826760 | C2 | semidirect |
| 5. #31826704 | C2 | semidirect |
| 6. #31826672 | C2 | semidirect |
| 7. #31826621 | C2 | semidirect |
| 8. C4×#17985382 | C2 | semidirect |
| 10. C2×#22583534 | C2 | semidirect |
| 92. D4×C283 | Q16 | semidirect |
| 122. C283 | #3299 | semidirect |
| 208. D4 | #17985382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827172 | 2 |
| #31826815 | 2 |
| #31826798 | 2 |
| #31826760 | 2 |
| #31826704 | 2 |
| #31826672 | 2 |
| #31826621 | 2 |
| C4×#17985382 | 2 |
| D4×C283⋊C8 | 2 |
| C2×#22583534 | 2 |
| D4×Q8×C283 | 2 |
| #3299 | 283 |