Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
452 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 137 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. #31827265 | C2 | semidirect |
| 2. C2×#22583632 | C2 | semidirect |
| 3. C2×#22583616 | C2 | semidirect |
| 4. #31826741 | C2 | semidirect |
| 5. #31826736 | C2 | semidirect |
| 6. #31826729 | C2 | semidirect |
| 7. #31826447 | C2 | semidirect |
| 8. C2×#108×C283 | C2 | semidirect |
| 20. C2×Dic1132 | C22 | semidirect |
| 21. C2×#17985381 | C22 | semidirect |
| 22. C2×D2264 | C22 | semidirect |
| 30. #22583528 | C22 | semidirect |
| 31. #22583526 | C22 | semidirect |
| 34. #108×C283 | C22 | semidirect |
| 35. #108×C283 | C22 | semidirect |
| 132. C283 | #3067 | semidirect |
| 140. C2×#108 | D283 | semidirect |
| 165. #108 | C2×D283 | semidirect |
| 166. #108 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827265 | 2 |
| C2×#22583632 | 2 |
| C2×#22583616 | 2 |
| #31826741 | 2 |
| #31826736 | 2 |
| #31826729 | 2 |
| #31826447 | 2 |
| C2×#108×C283 | 2 |
| #3067 | 283 |