Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 137 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. #31826873 | C2 | semidirect |
| 3. #31826871 | C2 | semidirect |
| 4. #31826869 | C2 | semidirect |
| 5. #31826867 | C2 | semidirect |
| 6. #31826866 | C2 | semidirect |
| 11. #500×C283 | C2 | semidirect |
| 42. #17985375 | Q8 | semidirect |
| 45. C8×D283 | Q8 | semidirect |
| 107. C283 | #3164 | semidirect |
| 113. #500 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827092 | 2 |
| #31826873 | 2 |
| #31826871 | 2 |
| #31826869 | 2 |
| #31826867 | 2 |
| #31826866 | 2 |
| #31826506 | 2 |
| #31826502 | 2 |
| #107×D283 | 2 |
| #31826419 | 2 |
| #500×C283 | 2 |
| #3164 | 283 |