Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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×#22583640 | C2 | semidirect |
| 2. C2×#22583597 | C2 | semidirect |
| 3. #41×Dic283 | C2 | semidirect |
| 4. #31826685 | C2 | semidirect |
| 5. #31826678 | C2 | semidirect |
| 6. #31826488 | C2 | semidirect |
| 7. #31826475 | C2 | semidirect |
| 8. #31826470 | C2 | semidirect |
| 12. C2×#17985382 | C22 | semidirect |
| 13. C2×#17985380 | C22 | semidirect |
| 18. Q8×Dic283 | C22 | semidirect |
| 20. D4×Dic283 | C22 | semidirect |
| 26. Dic283⋊C8 | C22 | semidirect |
| 27. #22583535 | C22 | semidirect |
| 125. C283 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583640 | 2 |
| C2×#22583597 | 2 |
| #41×Dic283 | 2 |
| #31826685 | 2 |
| #31826678 | 2 |
| #31826488 | 2 |
| #31826475 | 2 |
| #31826470 | 2 |
| C2×AGL(1,ℤ/8)×C283 | 2 |
| #3040 | 283 |