Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
784 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 4. #31826372 | C2 | semidirect |
| 5. #31826371 | C2 | semidirect |
| 6. #31826370 | C2 | semidirect |
| 7. #31826369 | C2 | semidirect |
| 9. #391×C283 | C2 | semidirect |
| 14. C2×Q8×D283 | C4 | semidirect |
| 122. C283 | #2310 | semidirect |
| 131. #391 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D283 | 2 |
| C2×#22583568 | 2 |
| C2×#22583567 | 2 |
| #31826372 | 2 |
| #31826371 | 2 |
| #31826370 | 2 |
| #31826369 | 2 |
| #31826327 | 2 |
| #391×C283 | 2 |
| #2310 | 283 |