Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
500 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 197 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. C4×#17985392 | C2 | semidirect |
| 3. C4×Dic1132 | C2 | semidirect |
| 4. C4×#17985381 | C2 | semidirect |
| 5. C4×D2264 | C2 | semidirect |
| 6. #31826503 | C2 | semidirect |
| 7. #31826462 | C2 | semidirect |
| 8. C2×C4×C8×C283 | C2 | semidirect |
| 10. #22583632 | C4 | direct (N × H) |
| 30. #17985392 | C2×C4 | semidirect |
| 36. Dic1132 | C2×C4 | semidirect |
| 37. #17985381 | C2×C4 | semidirect |
| 38. D2264 | C2×C4 | semidirect |
| 48. C2×C8×C283 | C2×C4 | semidirect |
| 83. C4×C283 | #135 | semidirect |
| 92. C283 | C4×#135 | semidirect |
| 101. C2×C4×C8 | D283 | semidirect |
| 135. C2×C8 | C4×D283 | semidirect |
| 178. C4 | #22583632 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583632 | 2 |
| C4×#17985392 | 2 |
| C4×Dic1132 | 2 |
| C4×#17985381 | 2 |
| C4×D2264 | 2 |
| #31826503 | 2 |
| #31826462 | 2 |
| C2×C4×C8×C283 | 2 |
| C4×#135 | 283 |