Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 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. #31827012 | C2 | semidirect |
| 2. #31826869 | C2 | semidirect |
| 3. #31826840 | C2 | semidirect |
| 4. #31826810 | C2 | semidirect |
| 5. #31826702 | C2 | semidirect |
| 6. #31826700 | C2 | semidirect |
| 7. #31826698 | C2 | semidirect |
| 8. C4×D2264 | C2 | semidirect |
| 9. C4×#17985377 | C2 | semidirect |
| 10. C4×C8×D283 | C2 | semidirect |
| 11. C4×D8×C283 | C2 | semidirect |
| 89. C4×D283 | D8 | semidirect |
| 91. C283⋊C8 | #41 | semidirect |
| 101. C8×C283 | #41 | semidirect |
| 127. C283 | #3169 | semidirect |
| 138. C4×D8 | D283 | semidirect |
| 229. C8 | #17985392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827012 | 2 |
| #31826869 | 2 |
| #31826840 | 2 |
| #31826810 | 2 |
| #31826702 | 2 |
| #31826700 | 2 |
| #31826698 | 2 |
| C4×D2264 | 2 |
| C4×#17985377 | 2 |
| C4×C8×D283 | 2 |
| C4×D8×C283 | 2 |
| #3169 | 283 |