Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 143 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. C22×Q8×D283 | C2 | semidirect |
| 2. C2×#22583642 | C2 | semidirect |
| 4. #31826620 | C2 | semidirect |
| 5. #31826619 | C2 | semidirect |
| 6. #31826606 | C2 | semidirect |
| 7. #31826605 | C2 | semidirect |
| 8. #31826604 | C2 | semidirect |
| 9. #31826472 | C2 | semidirect |
| 10. #31826427 | C2 | semidirect |
| 11. #451×C283 | C2 | semidirect |
| 23. C2×#17985382 | C22 | semidirect |
| 24. C2×#17985381 | C22 | semidirect |
| 25. C2×#17985379 | C22 | semidirect |
| 35. #22583535 | C22 | semidirect |
| 36. #22583534 | C22 | semidirect |
| 37. #22583533 | C22 | semidirect |
| 41. C2×Q16×C283 | C22 | semidirect |
| 43. #103×C283 | C22 | semidirect |
| 58. Q8×D283 | D4 | semidirect |
| 141. C22×C283 | #137 | semidirect |
| 152. C2×D283 | #137 | semidirect |
| 169. C283 | #3004 | semidirect |
| 176. #451 | D283 | semidirect |
| 195. C2×Q16 | C2×D283 | semidirect |
| 211. #103 | C2×D283 | semidirect |
| 321. C22 | #22583642 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D283 | 2 |
| C2×#22583642 | 2 |
| #31826978 | 2 |
| #31826620 | 2 |
| #31826619 | 2 |
| #31826606 | 2 |
| #31826605 | 2 |
| #31826604 | 2 |
| #31826472 | 2 |
| #31826427 | 2 |
| #451×C283 | 2 |
| #3004 | 283 |