Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 2. #31827039 | C2 | semidirect |
| 3. #31826948 | C2 | semidirect |
| 4. #31826689 | C2 | semidirect |
| 5. #31826682 | C2 | semidirect |
| 6. #31826673 | C2 | semidirect |
| 7. #31826668 | C2 | semidirect |
| 8. #31826493 | C2 | semidirect |
| 9. #31826467 | C2 | semidirect |
| 10. C2×#22583534 | C2 | semidirect |
| 11. C2×#137×C283 | C2 | semidirect |
| 146. C283 | #3046 | semidirect |
| 148. C2×#137 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583630 | 2 |
| #31827039 | 2 |
| #31826948 | 2 |
| #31826689 | 2 |
| #31826682 | 2 |
| #31826673 | 2 |
| #31826668 | 2 |
| #31826493 | 2 |
| #31826467 | 2 |
| C2×#22583534 | 2 |
| C2×#137×C283 | 2 |
| #3046 | 283 |