Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4×D1132 | C2 | semidirect |
| 2. #31826793 | C2 | semidirect |
| 3. #31826776 | C2 | semidirect |
| 4. #31826762 | C2 | semidirect |
| 5. #31826677 | C2 | semidirect |
| 6. #31826615 | C2 | semidirect |
| 8. #31826575 | C2 | semidirect |
| 9. #31826563 | C2 | semidirect |
| 10. #31826522 | C2 | semidirect |
| 11. #529×C283 | C2 | semidirect |
| 22. #22583543 | C22 | semidirect |
| 23. #22583541 | C22 | semidirect |
| 24. C4⋊(C283⋊C8) | C22 | semidirect |
| 25. #22583534 | C22 | semidirect |
| 26. #22583531 | C22 | semidirect |
| 31. #22583521 | C22 | semidirect |
| 33. #125×C283 | C22 | semidirect |
| 34. #124×C283 | C22 | semidirect |
| 38. C4×Q8×C283 | C22 | semidirect |
| 40. C4×D4×C283 | C22 | semidirect |
| 140. C283 | #3114 | semidirect |
| 142. #529 | D283 | semidirect |
| 158. #125 | C2×D283 | semidirect |
| 159. #124 | C2×D283 | semidirect |
| 163. C4×Q8 | C2×D283 | semidirect |
| 169. 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×C4×D1132 | 2 |
| #31826793 | 2 |
| #31826776 | 2 |
| #31826762 | 2 |
| #31826677 | 2 |
| #31826615 | 2 |
| #31826598 | 2 |
| #31826575 | 2 |
| #31826563 | 2 |
| #31826522 | 2 |
| #529×C283 | 2 |
| #3114 | 283 |