Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
472 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 2. C2×#22583616 | C2 | semidirect |
| 3. #31826583 | C2 | direct (N × H) |
| 4. C2×#22583546 | C2 | semidirect |
| 5. C2×#22583538 | C2 | semidirect |
| 6. C2×C4×C8×C283 | C2 | semidirect |
| 8. #22583632 | C4 | semidirect |
| 10. C2×Dic1132 | C4 | semidirect |
| 11. C2×#17985381 | C4 | semidirect |
| 12. C2×D2264 | C4 | semidirect |
| 14. #22583616 | C22 | semidirect |
| 18. #22583546 | C22 | semidirect |
| 19. #22583538 | C22 | semidirect |
| 23. C4×C8×C283 | C22 | semidirect |
| 32. Dic1132 | C2×C4 | semidirect |
| 33. #17985381 | C2×C4 | semidirect |
| 34. D2264 | C2×C4 | semidirect |
| 90. C2×C283 | #443 | semidirect |
| 93. C283 | C2×#443 | semidirect |
| 100. C2×C4×C8 | D283 | semidirect |
| 117. C4×C8 | C2×D283 | semidirect |
| 185. C2 | #31826583 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583632 | 2 |
| C2×#22583616 | 2 |
| #31826583 | 2 |
| C2×#22583546 | 2 |
| C2×#22583538 | 2 |
| C2×C4×C8×C283 | 2 |
| C2×#443 | 283 |