Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 141 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. #31827022 | C2 | semidirect |
| 3. #31826796 | C2 | semidirect |
| 4. #31826756 | C2 | semidirect |
| 5. #31826671 | C2 | semidirect |
| 7. C4×#17985381 | C2 | semidirect |
| 8. #431×C283 | C2 | semidirect |
| 12. #22583610 | C22 | semidirect |
| 13. #22583610 | C22 | semidirect |
| 18. C4×Dic566 | C22 | semidirect |
| 26. #22583542 | C22 | semidirect |
| 27. #22583535 | C22 | semidirect |
| 30. C4⋊C8×C283 | C22 | semidirect |
| 32. C4×C8×C283 | C22 | semidirect |
| 82. C2×C4×C283 | SD16 | semidirect |
| 112. C283 | #3101 | semidirect |
| 121. #431 | D283 | semidirect |
| 141. C4⋊C8 | C2×D283 | semidirect |
| 145. C4×C8 | C2×D283 | semidirect |
| 195. C2×C4 | #17985381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827022 | 2 |
| C2×C4×D1132 | 2 |
| #31826796 | 2 |
| #31826756 | 2 |
| #31826671 | 2 |
| #31826618 | 2 |
| C4×#17985381 | 2 |
| #431×C283 | 2 |
| #3101 | 283 |