Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
348 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31827193 | C2 | semidirect |
| 3. #31826820 | C2 | semidirect |
| 5. #31826766 | C2 | semidirect |
| 6. #31826751 | C2 | semidirect |
| 7. #31826688 | C2 | semidirect |
| 9. C4×Dic1132 | C2 | semidirect |
| 10. C4×#17985381 | C2 | semidirect |
| 11. C8×Q8×C283 | C2 | semidirect |
| 117. C283 | #3365 | semidirect |
| 127. C8×Q8 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827200 | 2 |
| #31827193 | 2 |
| #31826820 | 2 |
| #31826812 | 2 |
| #31826766 | 2 |
| #31826751 | 2 |
| #31826688 | 2 |
| #31826666 | 2 |
| C4×Dic1132 | 2 |
| C4×#17985381 | 2 |
| C8×Q8×C283 | 2 |
| #3365 | 283 |