Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
144 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 65 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. #31826881 | C2 | semidirect |
| 3. #31826285 | C2 | semidirect |
| 4. #31826250 | C2 | semidirect |
| 5. #31826249 | C2 | semidirect |
| 6. #31826240 | C2 | semidirect |
| 7. #504×C283 | C2 | semidirect |
| 71. C283 | #2171 | semidirect |
| 74. #504 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31826881 | 2 |
| #31826580 | 2 |
| #31826285 | 2 |
| #31826250 | 2 |
| #31826249 | 2 |
| #31826240 | 2 |
| #504×C283 | 2 |
| #2171 | 283 |