Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 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. #31826816 | C2 | semidirect |
| 4. #31826802 | C2 | semidirect |
| 5. #31826760 | C2 | semidirect |
| 6. #31826705 | C2 | semidirect |
| 7. #31826675 | C2 | semidirect |
| 8. #31826619 | C2 | semidirect |
| 10. #103×D283 | C2 | semidirect |
| 11. C4×Q16×C283 | C2 | semidirect |
| 81. D1132 | Q16 | semidirect |
| 122. C283 | #3299 | semidirect |
| 132. C4×Q16 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827175 | 2 |
| Q8×D1132 | 2 |
| #31826816 | 2 |
| #31826802 | 2 |
| #31826760 | 2 |
| #31826705 | 2 |
| #31826675 | 2 |
| #31826619 | 2 |
| C8×D1132 | 2 |
| #103×D283 | 2 |
| C4×Q16×C283 | 2 |
| #3299 | 283 |