Finite Group DatabasebetaFinite Group Databasebeta← C2×ΓL(1,𝔽8)×SL(2,ℤ/4) #72244682
Order 2016.
272 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 54 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. ΓL(1,𝔽8)×SL(2,ℤ/4) | C2 | direct (N × H) |
| 3. C2×C7×SL(2,ℤ/4) | C3 | semidirect |
| 5. C2×A4×ΓL(1,𝔽8) | C4 | semidirect |
| 13. C7×SL(2,ℤ/4) | C2×C3 | semidirect |
| 18. A4×ΓL(1,𝔽8) | C2×C4 | semidirect |
| 23. C2×C7×A4 | C3×C4 | semidirect |
| 28. C23×ΓL(1,𝔽8) | Dic3 | semidirect |
| 45. C2×SL(2,ℤ/4) | ΓL(1,𝔽8) | direct (N × H) |
| 49. C7×A4 | C2×C3×C4 | semidirect |
| 58. C22×ΓL(1,𝔽8) | C2×Dic3 | semidirect |
| 70. C23×C7 | C3×Dic3 | semidirect |
| 82. SL(2,ℤ/4) | C2×ΓL(1,𝔽8) | direct (N × H) |
| 92. C2×ΓL(1,𝔽8) | SL(2,ℤ/4) | direct (N × H) |
| 105. C22×C7 | C2×C3×Dic3 | semidirect |
| 116. C2×A4 | C4×ΓL(1,𝔽8) | semidirect |
| 126. ΓL(1,𝔽8) | C2×SL(2,ℤ/4) | direct (N × H) |
| 137. C2×C7 | C3×SL(2,ℤ/4) | semidirect |
| 151. A4 | C2×C4×ΓL(1,𝔽8) | semidirect |
| 159. C23 | Dic3×ΓL(1,𝔽8) | semidirect |
| 166. C7 | C2×C3×SL(2,ℤ/4) | semidirect |
| 183. C22 | C2×Dic3×ΓL(1,𝔽8) | semidirect |
| 193. C2 | ΓL(1,𝔽8)×SL(2,ℤ/4) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×A4×ΓL(1,𝔽8) | 2 |
| ΓL(1,𝔽8)×SL(2,ℤ/4) | 2 |
| C2×C7×SL(2,ℤ/4) | 3 |
| C2×C22⋊C4×ΓL(1,𝔽8) | 3 |
| C2×Dic3×ΓL(1,𝔽8) | 4 |
| C2×C3×SL(2,ℤ/4) | 7 |