Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 115 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. #31827189 | C2 | semidirect |
| 2. #31827130 | C2 | semidirect |
| 3. #31826826 | C2 | semidirect |
| 4. #31826758 | C2 | semidirect |
| 5. #31826742 | C2 | semidirect |
| 7. #31826667 | C2 | semidirect |
| 8. #31826595 | C2 | semidirect |
| 9. #31826568 | C2 | semidirect |
| 11. #487×C283 | C2 | semidirect |
| 122. C283 | #3367 | semidirect |
| 127. #487 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827189 | 2 |
| #31827130 | 2 |
| #31826826 | 2 |
| #31826758 | 2 |
| #31826742 | 2 |
| #31826683 | 2 |
| #31826667 | 2 |
| #31826595 | 2 |
| #31826568 | 2 |
| C4×D2264 | 2 |
| #487×C283 | 2 |
| #3367 | 283 |