Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 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. #31826947 | C2 | semidirect |
| 3. #31826578 | C2 | semidirect |
| 4. #31826576 | C2 | semidirect |
| 5. #31826572 | C2 | semidirect |
| 6. C4×#17985379 | C2 | semidirect |
| 7. #31826550 | C2 | semidirect |
| 8. #106×D283 | C2 | semidirect |
| 9. #31826465 | C2 | semidirect |
| 10. #31826422 | C2 | semidirect |
| 11. #441×C283 | C2 | semidirect |
| 13. #22583633 | C4 | semidirect |
| 41. #17985393 | C2×C4 | semidirect |
| 49. #17985379 | C2×C4 | semidirect |
| 50. D2264 | C2×C4 | semidirect |
| 54. C8×D283 | C2×C4 | semidirect |
| 65. Q16×C283 | C2×C4 | semidirect |
| 114. C283 | #2952 | semidirect |
| 121. #441 | D283 | semidirect |
| 165. Q16 | C4×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583633 | 2 |
| #31826947 | 2 |
| #31826578 | 2 |
| #31826576 | 2 |
| #31826572 | 2 |
| C4×#17985379 | 2 |
| #31826550 | 2 |
| #106×D283 | 2 |
| #31826465 | 2 |
| #31826422 | 2 |
| #441×C283 | 2 |
| #2952 | 283 |