Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 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. #31827020 | C2 | semidirect |
| 3. #31826828 | C2 | semidirect |
| 4. #31826813 | C2 | semidirect |
| 5. #31826812 | C2 | semidirect |
| 6. #31826811 | C2 | semidirect |
| 7. #31826468 | C2 | semidirect |
| 8. C4×#17985375 | C2 | semidirect |
| 9. #486×C283 | C2 | semidirect |
| 14. #22583610 | C22 | semidirect |
| 19. #22583601 | C22 | semidirect |
| 26. #22583532 | C22 | semidirect |
| 27. #22583531 | C22 | semidirect |
| 28. #22583530 | C22 | semidirect |
| 29. #22583520 | C22 | semidirect |
| 30. C4×C283⋊C8 | C22 | semidirect |
| 31. C4⋊Q8×C283 | C22 | semidirect |
| 33. #102×C283 | C22 | semidirect |
| 34. C4×C8×C283 | C22 | semidirect |
| 123. C283 | #3138 | semidirect |
| 131. #486 | D283 | semidirect |
| 139. C4⋊Q8 | C2×D283 | semidirect |
| 155. #102 | C2×D283 | semidirect |
| 158. C4×C8 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827020 | 2 |
| #127×D283 | 2 |
| #31826828 | 2 |
| #31826813 | 2 |
| #31826812 | 2 |
| #31826811 | 2 |
| #31826468 | 2 |
| C4×#17985375 | 2 |
| #486×C283 | 2 |
| #3138 | 283 |