Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
466 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 145 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. #31827263 | C2 | semidirect |
| 2. C2×#22583638 | C2 | semidirect |
| 3. C2×#22583635 | C2 | semidirect |
| 4. #31826735 | C2 | semidirect |
| 5. #31826728 | C2 | semidirect |
| 6. #31826514 | C2 | semidirect |
| 7. #31826447 | C2 | semidirect |
| 8. C2×#22583526 | C2 | semidirect |
| 9. #568×C283 | C2 | semidirect |
| 13. #22583640 | C22 | semidirect |
| 19. #22583635 | C22 | semidirect |
| 21. C2×#17985381 | C22 | semidirect |
| 23. C2×D2264 | C22 | semidirect |
| 27. #22583546 | C22 | semidirect |
| 28. #22583528 | C22 | semidirect |
| 29. #22583526 | C22 | semidirect |
| 30. #22583526 | C22 | semidirect |
| 33. #131×C283 | C22 | semidirect |
| 147. C283 | #3068 | semidirect |
| 152. #568 | D283 | semidirect |
| 175. #131 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827263 | 2 |
| C2×#22583638 | 2 |
| C2×#22583635 | 2 |
| #31826735 | 2 |
| #31826728 | 2 |
| #31826514 | 2 |
| #31826447 | 2 |
| C2×#22583526 | 2 |
| #568×C283 | 2 |
| #3068 | 283 |