Finite Group DatabasebetaFinite Group Databasebeta← C4×C22⋊C4×ΓL(1,𝔽8) #13054908
Order 1344.
516 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 219 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 |
|---|---|---|
| 3. C2×C42×ΓL(1,𝔽8) | C2 | semidirect |
| 4. ΓL(1,𝔽8)×#95 | C2 | semidirect |
| 5. C4×C7×C22⋊C4 | C3 | semidirect |
| 8. C22×C4×ΓL(1,𝔽8) | C4 | semidirect |
| 12. C22⋊C4×ΓL(1,𝔽8) | C4 | direct (N × H) |
| 16. C2×C42×C7 | C2×C3 | semidirect |
| 17. C7×#95 | C2×C3 | semidirect |
| 30. C2×C4×ΓL(1,𝔽8) | C2×C4 | semidirect |
| 34. C22×C4×C7 | C3×C4 | semidirect |
| 38. C7×C22⋊C4 | C3×C4 | semidirect |
| 47. C22×ΓL(1,𝔽8) | C42 | semidirect |
| 54. C4×ΓL(1,𝔽8) | C22⋊C4 | direct (N × H) |
| 55. C4×C22⋊C4 | ΓL(1,𝔽8) | direct (N × H) |
| 67. C2×C4×C7 | C2×C3×C4 | semidirect |
| 84. C2×C42 | C2×ΓL(1,𝔽8) | semidirect |
| 85. #95 | C2×ΓL(1,𝔽8) | semidirect |
| 89. C22×C7 | C3×C42 | semidirect |
| 96. C4×C7 | C3×C22⋊C4 | semidirect |
| 110. ΓL(1,𝔽8) | C4×C22⋊C4 | direct (N × H) |
| 113. C22×C4 | C4×ΓL(1,𝔽8) | semidirect |
| 117. C22⋊C4 | C4×ΓL(1,𝔽8) | direct (N × H) |
| 146. C2×C4 | C2×C4×ΓL(1,𝔽8) | semidirect |
| 148. C7 | C3×C4×C22⋊C4 | semidirect |
| 157. C22 | C42×ΓL(1,𝔽8) | semidirect |
| 164. C4 | C22⋊C4×ΓL(1,𝔽8) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×ΓL(1,𝔽8) | 2 |
| C2×C22⋊C4×ΓL(1,𝔽8) | 2 |
| C2×C42×ΓL(1,𝔽8) | 2 |
| ΓL(1,𝔽8)×#95 | 2 |
| C4×C7×C22⋊C4 | 3 |
| C3×C4×C22⋊C4 | 7 |