Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
572 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 572 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. C2×#22583633 | C2 | semidirect |
| 2. C2×#22583631 | C2 | semidirect |
| 3. C2×#22583629 | C2 | semidirect |
| 4. #31827014 | C2 | semidirect |
| 5. #31826849 | C2 | semidirect |
| 6. #31826847 | C2 | semidirect |
| 7. #31826843 | C2 | semidirect |
| 8. #31826840 | C2 | semidirect |
| 9. #31826836 | C2 | semidirect |
| 10. C4×C8×D283 | C2 | semidirect |
| 11. #495×C283 | C2 | semidirect |
| 62. C8×D283 | D4 | semidirect |
| 63. C8×D283 | D4 | semidirect |
| 119. Dic283 | #135 | semidirect |
| 125. C283 | #3147 | semidirect |
| 133. #495 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583633 | 2 |
| C2×#22583631 | 2 |
| C2×#22583629 | 2 |
| #31827014 | 2 |
| #31826849 | 2 |
| #31826847 | 2 |
| #31826843 | 2 |
| #31826840 | 2 |
| #31826836 | 2 |
| C4×C8×D283 | 2 |
| #495×C283 | 2 |
| #3147 | 283 |