Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
412 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 129 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. #31827020 | C2 | semidirect |
| 3. #31826861 | C2 | semidirect |
| 4. #31826839 | C2 | semidirect |
| 5. #31826812 | C2 | semidirect |
| 6. #31826697 | C2 | semidirect |
| 7. #31826550 | C2 | semidirect |
| 8. C4×C8×D283 | C2 | semidirect |
| 9. #487×C283 | C2 | semidirect |
| 81. C4×D283 | SD16 | semidirect |
| 82. C283⋊C8 | #41 | semidirect |
| 112. C283 | #3167 | semidirect |
| 118. #487 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827020 | 2 |
| #31827016 | 2 |
| #31826861 | 2 |
| #31826839 | 2 |
| #31826812 | 2 |
| #31826697 | 2 |
| #31826550 | 2 |
| C4×C8×D283 | 2 |
| #487×C283 | 2 |
| #3167 | 283 |