Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
172 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 53 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. #31826751 | C2 | semidirect |
| 4. #31826589 | C2 | semidirect |
| 5. #31826215 | C2 | semidirect |
| 6. #31826212 | C2 | semidirect |
| 45. Dic566 | SD16 | semidirect |
| 51. C283⋊C8 | SD16 | semidirect |
| 79. C283 | #1666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31826837 | 2 |
| #31826751 | 2 |
| #31826662 | 2 |
| #31826589 | 2 |
| #31826215 | 2 |
| #31826212 | 2 |
| #331×C283 | 2 |
| #1666 | 283 |