Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22583640 | C2 | semidirect |
| 3. C2×#22583598 | C2 | semidirect |
| 4. #31826687 | C2 | semidirect |
| 5. #31826680 | C2 | semidirect |
| 6. #31826489 | C2 | semidirect |
| 7. #31826473 | C2 | semidirect |
| 8. #31826469 | C2 | semidirect |
| 9. C4×#41×C283 | C2 | semidirect |
| 14. C2×#17985382 | C22 | semidirect |
| 15. C2×#17985380 | C22 | semidirect |
| 24. C4⋊(C283⋊C8) | C22 | semidirect |
| 25. #22583533 | C22 | semidirect |
| 28. C4×Q8×C283 | C22 | semidirect |
| 30. C4×D4×C283 | C22 | semidirect |
| 125. C283 | #3040 | semidirect |
| 130. C4×#41 | D283 | semidirect |
| 150. C4×Q8 | C2×D283 | semidirect |
| 152. C4×D4 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583640 | 2 |
| C2×#22583635 | 2 |
| C2×#22583598 | 2 |
| #31826687 | 2 |
| #31826680 | 2 |
| #31826489 | 2 |
| #31826473 | 2 |
| #31826469 | 2 |
| C4×#41×C283 | 2 |
| #3040 | 283 |