Finite Group DatabasebetaFinite Group Databasebeta← C22×C4⋊(ΓL(1,𝔽8)⋊C4) #13057519
Order 1344.
836 conjugacy classes of subgroups; only the 456 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 456 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×C4⋊(ΓL(1,𝔽8)⋊C4) | C2 | direct (N × H) |
| 4. C22×C4⋊Dic7 | C3 | semidirect |
| 6. C22×C4×ΓL(1,𝔽8) | C4 | semidirect |
| 10. C4⋊(ΓL(1,𝔽8)⋊C4) | C22 | direct (N × H) |
| 13. C2×C4⋊Dic7 | C2×C3 | semidirect |
| 19. C2×C4×ΓL(1,𝔽8) | C2×C4 | semidirect |
| 24. C22×C4×C7 | C3×C4 | semidirect |
| 28. C4⋊Dic7 | C22×C3 | semidirect |
| 32. C22×ΓL(1,𝔽8) | C4⋊C4 | semidirect |
| 37. C4×ΓL(1,𝔽8) | C22×C4 | semidirect |
| 44. C2×C4×C7 | C2×C3×C4 | semidirect |
| 54. C2×ΓL(1,𝔽8) | C2×C4⋊C4 | semidirect |
| 61. C22×C7 | C3×C4⋊C4 | semidirect |
| 66. C4×C7 | C22×C3×C4 | semidirect |
| 76. ΓL(1,𝔽8) | C22×C4⋊C4 | semidirect |
| 80. C22×C4 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 83. C2×C7 | C2×C3×C4⋊C4 | semidirect |
| 100. C2×C4 | C2×ΓL(1,𝔽8)⋊C4 | semidirect |
| 102. C7 | C22×C3×C4⋊C4 | semidirect |
| 107. C22 | C4⋊(ΓL(1,𝔽8)⋊C4) | direct (N × H) |
| 113. C4 | C22×ΓL(1,𝔽8)⋊C4 | semidirect |
| 115. C2 | C2×C4⋊(ΓL(1,𝔽8)⋊C4) | 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 |
| C23×ΓL(1,𝔽8)⋊C4 | 2 |
| C2×C4⋊(ΓL(1,𝔽8)⋊C4) | 2 |
| C22×C4⋊Dic7 | 3 |
| C22×C3×C4⋊C4 | 7 |