Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
612 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 205 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. C2×C4×Dic566 | C2 | semidirect |
| 3. #31826370 | C2 | semidirect |
| 5. #31826353 | C2 | semidirect |
| 6. #31826338 | C2 | semidirect |
| 7. #31826334 | C2 | semidirect |
| 8. #31826311 | C2 | semidirect |
| 11. #22583597 | C4 | semidirect |
| 32. C2×Dic566 | C2×C4 | semidirect |
| 41. C22⋊Dic283 | C2×C4 | semidirect |
| 44. C4×Dic283 | C2×C4 | semidirect |
| 111. C283 | #2326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583597 | 2 |
| C2×C4×Dic566 | 2 |
| #31826370 | 2 |
| #31826368 | 2 |
| #31826353 | 2 |
| #31826338 | 2 |
| #31826334 | 2 |
| #31826311 | 2 |
| C2×C4×D4×C283 | 2 |
| #2326 | 283 |