Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 1. #31827181 | C2 | semidirect |
| 2. #31827135 | C2 | semidirect |
| 3. #31826788 | C2 | semidirect |
| 4. #31826757 | C2 | semidirect |
| 5. #31826700 | C2 | semidirect |
| 6. #31826657 | C2 | semidirect |
| 7. #31826611 | C2 | semidirect |
| 8. C4×#17985381 | C2 | semidirect |
| 9. C8×D1132 | C2 | semidirect |
| 10. #31826458 | C2 | semidirect |
| 11. #486×C283 | C2 | semidirect |
| 132. C283 | #3305 | semidirect |
| 136. #486 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827181 | 2 |
| #31827135 | 2 |
| #31826788 | 2 |
| #31826757 | 2 |
| #31826700 | 2 |
| #31826657 | 2 |
| #31826611 | 2 |
| C4×#17985381 | 2 |
| C8×D1132 | 2 |
| #31826458 | 2 |
| #486×C283 | 2 |
| #3305 | 283 |