Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. Q8×D1132 | C2 | semidirect |
| 3. #31826816 | C2 | semidirect |
| 4. #31826797 | C2 | semidirect |
| 5. #31826750 | C2 | semidirect |
| 6. #31826693 | C2 | semidirect |
| 7. #31826670 | C2 | semidirect |
| 8. #31826602 | C2 | semidirect |
| 9. C8×D1132 | C2 | semidirect |
| 10. #103×D283 | C2 | semidirect |
| 11. C4×SD16×C283 | C2 | semidirect |
| 82. D1132 | SD16 | semidirect |
| 94. Q8×C283 | #41 | semidirect |
| 128. C283 | #3298 | semidirect |
| 138. C4×SD16 | D283 | semidirect |
| 213. Q8 | #17985392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D1132 | 2 |
| #31827120 | 2 |
| #31826816 | 2 |
| #31826797 | 2 |
| #31826750 | 2 |
| #31826693 | 2 |
| #31826670 | 2 |
| #31826602 | 2 |
| C8×D1132 | 2 |
| #103×D283 | 2 |
| C4×SD16×C283 | 2 |
| #3298 | 283 |