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. #29510213 | C2 | semidirect |
| 4. #29510204 | C2 | semidirect |
| 5. #29510203 | C2 | semidirect |
| 6. #29510200 | C2 | semidirect |
| 7. #29510193 | C2 | semidirect |
| 8. #29510172 | C2 | semidirect |
| 9. C4⋊Q8×C487 | C2 | semidirect |
| 63. C487 | #536 | semidirect |
| 68. C4⋊Q8 | D487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21441262 | 2 |
| C2×Q8×D487 | 2 |
| #29510213 | 2 |
| #29510204 | 2 |
| #29510203 | 2 |
| #29510200 | 2 |
| #29510193 | 2 |
| #29510172 | 2 |
| C4⋊Q8×C487 | 2 |
| #536 | 487 |