Finite Group DatabasebetaFinite Group DatabasebetaOrder 31168.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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×Q8×D487 | C2 | semidirect |
| 3. #29510214 | C2 | semidirect |
| 4. #29510201 | C2 | semidirect |
| 5. #29510200 | C2 | semidirect |
| 6. #29510197 | C2 | semidirect |
| 7. #29510195 | C2 | semidirect |
| 8. #29510194 | C2 | semidirect |
| 9. #29510191 | C2 | semidirect |
| 10. #29510173 | C2 | semidirect |
| 11. C22⋊Q8×C487 | C2 | semidirect |
| 83. C487 | #536 | semidirect |
| 94. C22⋊Q8 | D487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21441261 | 2 |
| C2×Q8×D487 | 2 |
| #29510214 | 2 |
| #29510201 | 2 |
| #29510200 | 2 |
| #29510197 | 2 |
| #29510195 | 2 |
| #29510194 | 2 |
| #29510191 | 2 |
| #29510173 | 2 |
| C22⋊Q8×C487 | 2 |
| #536 | 487 |