Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31827194 | C2 | semidirect |
| 3. #31826821 | C2 | semidirect |
| 5. #31826768 | C2 | semidirect |
| 6. #31826750 | C2 | semidirect |
| 7. #31826689 | C2 | semidirect |
| 9. C8×Dic566 | C2 | semidirect |
| 10. #31826550 | C2 | semidirect |
| 11. C4×Q16×C283 | C2 | semidirect |
| 117. C283 | #3365 | semidirect |
| 128. C4×Q16 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827200 | 2 |
| #31827194 | 2 |
| #31826821 | 2 |
| #31826812 | 2 |
| #31826768 | 2 |
| #31826750 | 2 |
| #31826689 | 2 |
| #31826665 | 2 |
| C8×Dic566 | 2 |
| #31826550 | 2 |
| C4×Q16×C283 | 2 |
| #3365 | 283 |