Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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. #31827282 | C2 | semidirect |
| 2. #31827270 | C2 | semidirect |
| 3. #31826908 | C2 | semidirect |
| 4. #31826903 | C2 | semidirect |
| 5. #31826897 | C2 | semidirect |
| 6. C2×#22583555 | C2 | semidirect |
| 7. #504×C283 | C2 | semidirect |
| 13. #22583632 | C22 | semidirect |
| 14. C2×Dic1132 | C22 | semidirect |
| 16. Dic2264 | C22 | semidirect |
| 17. #22583555 | C22 | semidirect |
| 18. #22583555 | C22 | semidirect |
| 19. #22583555 | C22 | semidirect |
| 20. D4528 | C22 | semidirect |
| 22. M32×C283 | C22 | semidirect |
| 23. C2×C16×C283 | C22 | semidirect |
| 74. C283 | #3416 | semidirect |
| 82. #504 | D283 | semidirect |
| 97. M32 | C2×D283 | semidirect |
| 98. C2×C16 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827282 | 2 |
| #31827270 | 2 |
| #31826908 | 2 |
| #31826903 | 2 |
| #31826897 | 2 |
| C2×#22583555 | 2 |
| #504×C283 | 2 |
| #3416 | 283 |