Finite Group DatabasebetaFinite Group DatabasebetaOrder 31168.
210 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C487 | C22⋊C4 |
| commutator | C22 | C22×C4×C487 |
| Frattini, cosocle | C23 | C23×C487 |
| prime radical | C22×D4×C487 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C487 ◁ C24×C487 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C22⋊C4×C487 | C2 | semidirect |
| 3. #99×C487 | C2 | direct (N × H) |
| 4. C24×C487 | C4 | semidirect |
| 8. C2×D4×C487 | C4 | semidirect |
| 11. C22×C4×C487 | C4 | semidirect |
| 13. C22⋊C4×C487 | C22 | semidirect |
| 20. C23×C487 | C2×C4 | semidirect |
| 30. C2×C4×C487 | C2×C4 | semidirect |
| 52. C2×C487 | #99 | direct (N × H) |
| 54. C487 | C2×#99 | direct (N × H) |
| 55. C2×#99 | C487 | direct (N × H) |
| 57. C2×C22⋊C4 | C2×C487 | semidirect |
| 58. #99 | C2×C487 | direct (N × H) |
| 59. C24 | C4×C487 | semidirect |
| 63. C2×D4 | C4×C487 | semidirect |
| 66. C22×C4 | C4×C487 | semidirect |
| 68. C22⋊C4 | C22×C487 | semidirect |
| 75. C23 | C2×C4×C487 | semidirect |
| 85. C2×C4 | C2×C4×C487 | semidirect |
| 107. C2 | #99×C487 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×C487 | 2 |
| C2×C22⋊C4×C487 | 2 |
| #99×C487 | 2 |
| C2×#99 | 487 |