Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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. #31826816 | C2 | semidirect |
| 4. #31826801 | C2 | semidirect |
| 5. #31826761 | C2 | semidirect |
| 6. #31826706 | C2 | semidirect |
| 7. #31826676 | C2 | semidirect |
| 8. #31826623 | C2 | semidirect |
| 9. C4×Dic1132 | C2 | semidirect |
| 10. C2×#22583535 | C2 | semidirect |
| 93. D4×C283 | Q16 | semidirect |
| 122. C283 | #3299 | semidirect |
| 208. D4 | Dic1132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827172 | 2 |
| D4×Dic566 | 2 |
| #31826816 | 2 |
| #31826801 | 2 |
| #31826761 | 2 |
| #31826706 | 2 |
| #31826676 | 2 |
| #31826623 | 2 |
| C4×Dic1132 | 2 |
| C2×#22583535 | 2 |
| C8×D4×C283 | 2 |
| #3299 | 283 |