Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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. #31826838 | C2 | semidirect |
| 3. #31826760 | C2 | semidirect |
| 4. #31826756 | C2 | semidirect |
| 5. #31826208 | C2 | semidirect |
| 6. #31826194 | C2 | semidirect |
| 7. Q8⋊C8×C283 | C2 | semidirect |
| 69. Q8×C283 | SD16 | semidirect |
| 98. C283 | #1631 | semidirect |
| 105. Q8⋊C8 | D283 | semidirect |
| 153. Q8 | #17985381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827137 | 2 |
| #31826838 | 2 |
| #31826760 | 2 |
| #31826756 | 2 |
| #31826208 | 2 |
| #31826194 | 2 |
| Q8⋊C8×C283 | 2 |
| #1631 | 283 |