Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
326 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 67 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. #31826505 | C2 | semidirect |
| 3. C2×#22583537 | C2 | semidirect |
| 4. C2×#22583526 | C2 | semidirect |
| 5. #31826366 | C2 | semidirect |
| 6. #31826226 | C2 | semidirect |
| 7. #417×C283 | C2 | semidirect |
| 38. #17985376 | D4 | semidirect |
| 130. C283 | #2037 | semidirect |
| 135. #417 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827029 | 2 |
| #31826505 | 2 |
| C2×#22583537 | 2 |
| C2×#22583526 | 2 |
| #31826366 | 2 |
| #31826226 | 2 |
| #417×C283 | 2 |
| #2037 | 283 |