Finite Group DatabasebetaFinite Group DatabasebetaOrder 31168.
218 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 95 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. #29510210 | C2 | semidirect |
| 2. #29510205 | C2 | semidirect |
| 3. #29510200 | C2 | semidirect |
| 4. #29510198 | C2 | semidirect |
| 5. #29510194 | C2 | semidirect |
| 6. #29510193 | C2 | semidirect |
| 8. C4×C22⋊D487 | C2 | semidirect |
| 9. C2×C4⋊C4×C487 | C2 | semidirect |
| 66. C487 | #539 | semidirect |
| 76. C2×C4⋊C4 | D487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29510210 | 2 |
| #29510205 | 2 |
| #29510200 | 2 |
| #29510198 | 2 |
| #29510194 | 2 |
| #29510193 | 2 |
| #29510189 | 2 |
| C4×C22⋊D487 | 2 |
| C2×C4⋊C4×C487 | 2 |
| #539 | 487 |