Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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. #31826809 | C2 | semidirect |
| 4. #31826808 | C2 | semidirect |
| 5. #31826802 | C2 | semidirect |
| 6. #31826797 | C2 | semidirect |
| 7. #31826508 | C2 | semidirect |
| 8. #31826473 | C2 | semidirect |
| 9. C2×#22583535 | C2 | semidirect |
| 11. #427×C283 | C2 | semidirect |
| 126. C283 | #3097 | semidirect |
| 135. #427 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827041 | 2 |
| #31826945 | 2 |
| #31826809 | 2 |
| #31826808 | 2 |
| #31826802 | 2 |
| #31826797 | 2 |
| #31826508 | 2 |
| #31826473 | 2 |
| C2×#22583535 | 2 |
| #31826431 | 2 |
| #427×C283 | 2 |
| #3097 | 283 |