Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. C2×#22583534 | C2 | semidirect |
| 4. C2×#22583529 | C2 | semidirect |
| 5. #31826233 | C2 | semidirect |
| 6. #31826229 | C2 | semidirect |
| 24. #137×C283 | C4 | semidirect |
| 116. C283 | #1908 | semidirect |
| 128. #137 | Dic283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583617 | 2 |
| #31826466 | 2 |
| C2×#22583534 | 2 |
| C2×#22583529 | 2 |
| #31826233 | 2 |
| #31826229 | 2 |
| C2×#137×C283 | 2 |
| #1908 | 283 |