Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×Dic566 | C2 | semidirect |
| 3. #31826812 | C2 | semidirect |
| 4. #31826810 | C2 | semidirect |
| 5. #31826755 | C2 | semidirect |
| 6. #31826754 | C2 | semidirect |
| 7. #31826665 | C2 | semidirect |
| 8. #31826663 | C2 | semidirect |
| 9. C8×Dic566 | C2 | semidirect |
| 10. #31826550 | C2 | semidirect |
| 11. C4×SD16×C283 | C2 | semidirect |
| 77. Dic566 | SD16 | semidirect |
| 91. Q8×C283 | #41 | semidirect |
| 125. C283 | #3362 | semidirect |
| 137. C4×SD16 | D283 | semidirect |
| 206. Q8 | #17985392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic566 | 2 |
| #31827136 | 2 |
| #31826812 | 2 |
| #31826810 | 2 |
| #31826755 | 2 |
| #31826754 | 2 |
| #31826665 | 2 |
| #31826663 | 2 |
| C8×Dic566 | 2 |
| #31826550 | 2 |
| C4×SD16×C283 | 2 |
| #3362 | 283 |