Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
376 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 3. #31826771 | C2 | semidirect |
| 4. #31826770 | C2 | semidirect |
| 5. #31826757 | C2 | semidirect |
| 6. #31826751 | C2 | semidirect |
| 7. #31826750 | C2 | semidirect |
| 11. #477×C283 | C2 | semidirect |
| 47. Q8×D283 | Q8 | semidirect |
| 130. C283 | #3078 | semidirect |
| 137. #477 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827020 | 2 |
| C4×Q8×D283 | 2 |
| #31826771 | 2 |
| #31826770 | 2 |
| #31826757 | 2 |
| #31826751 | 2 |
| #31826750 | 2 |
| #31826506 | 2 |
| #31826487 | 2 |
| #31826472 | 2 |
| #477×C283 | 2 |
| #3078 | 283 |