Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 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×#22583638 | C2 | semidirect |
| 2. C2×#22583635 | C2 | semidirect |
| 3. #31827011 | C2 | semidirect |
| 4. C2×#22583572 | C2 | semidirect |
| 5. #31826683 | C2 | semidirect |
| 6. #31826679 | C2 | semidirect |
| 7. #31826669 | C2 | semidirect |
| 8. #31826659 | C2 | semidirect |
| 9. #31826488 | C2 | semidirect |
| 10. #31826464 | C2 | semidirect |
| 11. #417×C283 | C2 | semidirect |
| 22. #22583608 | C22 | semidirect |
| 23. #22583606 | C22 | semidirect |
| 24. #22583599 | C22 | semidirect |
| 25. #22583597 | C22 | semidirect |
| 36. Dic283⋊C8 | C22 | semidirect |
| 37. Dic283⋊C8 | C22 | semidirect |
| 38. #22583533 | C22 | semidirect |
| 39. #22583530 | C22 | semidirect |
| 43. #103×C283 | C22 | semidirect |
| 44. #102×C283 | C22 | semidirect |
| 51. C2×D1132 | D4 | semidirect |
| 158. Dic283 | AGL(1,ℤ/8) | semidirect |
| 166. C283 | #3036 | semidirect |
| 178. #417 | D283 | semidirect |
| 209. #103 | C2×D283 | semidirect |
| 211. #102 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583638 | 2 |
| C2×#22583635 | 2 |
| #31827011 | 2 |
| C2×#22583572 | 2 |
| #31826683 | 2 |
| #31826679 | 2 |
| #31826669 | 2 |
| #31826659 | 2 |
| #31826488 | 2 |
| #31826464 | 2 |
| #417×C283 | 2 |
| #3036 | 283 |