Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D283 | C2 | semidirect |
| 3. #31826761 | C2 | semidirect |
| 4. #31826757 | C2 | semidirect |
| 5. #31826755 | C2 | semidirect |
| 6. #31826749 | C2 | semidirect |
| 7. #31826743 | C2 | semidirect |
| 8. #31826504 | C2 | semidirect |
| 9. #31826487 | C2 | semidirect |
| 11. #476×C283 | C2 | semidirect |
| 44. #17985391 | Q8 | semidirect |
| 86. Dic566 | C2×Q8 | semidirect |
| 105. D4×C283 | C2×Q8 | semidirect |
| 137. C283 | #3079 | semidirect |
| 144. #476 | D283 | semidirect |
| 229. D4 | Q8×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D283 | 2 |
| C4×#17985391 | 2 |
| #31826761 | 2 |
| #31826757 | 2 |
| #31826755 | 2 |
| #31826749 | 2 |
| #31826743 | 2 |
| #31826504 | 2 |
| #31826487 | 2 |
| #31826463 | 2 |
| #476×C283 | 2 |
| #3079 | 283 |