Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#22583657 | C2 | semidirect |
| 2. C22×#17985380 | C2 | semidirect |
| 3. #31827032 | C2 | semidirect |
| 4. #31826607 | C2 | semidirect |
| 5. #31826602 | C2 | semidirect |
| 6. #31826475 | C2 | semidirect |
| 7. #31826461 | C2 | semidirect |
| 8. #31826433 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C283 | C2 | semidirect |
| 15. C2×#17985391 | C22 | semidirect |
| 18. C2×Q8×D283 | C22 | semidirect |
| 27. #22583535 | C22 | semidirect |
| 28. #22583534 | C22 | semidirect |
| 29. #22583531 | C22 | semidirect |
| 30. (C2×D283)⋊C8 | C22 | semidirect |
| 48. C2×Dic566 | D4 | semidirect |
| 69. #41×C283 | D4 | semidirect |
| 145. C283 | #3010 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D283 | semidirect |
| 191. #41 | C22⋊D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583657 | 2 |
| C22×#17985380 | 2 |
| #31827032 | 2 |
| #31826607 | 2 |
| #31826602 | 2 |
| #31826475 | 2 |
| #31826461 | 2 |
| #31826433 | 2 |
| C2×AGL(1,ℤ/8)×C283 | 2 |
| #3010 | 283 |