Finite Group DatabasebetaFinite Group DatabasebetaOrder 31168.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #29510263 | C2 | semidirect |
| 2. #29510262 | C2 | semidirect |
| 3. #29510248 | C2 | semidirect |
| 4. #29510247 | C2 | semidirect |
| 5. #29510244 | C2 | semidirect |
| 6. #29510236 | C2 | semidirect |
| 7. #29510235 | C2 | semidirect |
| 8. C2×#21441251 | C2 | semidirect |
| 9. Q16×D487 | C2 | semidirect |
| 10. #29510223 | C2 | semidirect |
| 11. #137×C487 | C2 | semidirect |
| 87. C487 | #578 | semidirect |
| 94. #137 | D487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29510263 | 2 |
| #29510262 | 2 |
| #29510248 | 2 |
| #29510247 | 2 |
| #29510244 | 2 |
| #29510236 | 2 |
| #29510235 | 2 |
| C2×#21441251 | 2 |
| Q16×D487 | 2 |
| #29510223 | 2 |
| #137×C487 | 2 |
| #578 | 487 |