Finite Group DatabasebetaFinite Group Databasebeta← C22×C4×ΓL(1,𝔽8)⋊C4 #13057516
Order 1344.
996 conjugacy classes of subgroups; only the 616 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 616 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 |
| 8. C22×ΓL(1,𝔽8)⋊C4 | C4 | direct (N × H) |
| 10. C4×ΓL(1,𝔽8)⋊C4 | C22 | direct (N × H) |
| 13. C2×C4×Dic7 | C2×C3 | semidirect |
| 18. C2×C4×ΓL(1,𝔽8) | C2×C4 | semidirect |
| 20. C2×ΓL(1,𝔽8)⋊C4 | C2×C4 | direct (N × H) |
| 23. C22×C4×C7 | C3×C4 | semidirect |
| 25. C22×Dic7 | C3×C4 | semidirect |
| 27. C4×Dic7 | C22×C3 | semidirect |
| 31. C22×ΓL(1,𝔽8) | C42 | semidirect |
| 35. C4×ΓL(1,𝔽8) | C22×C4 | semidirect |
| 36. ΓL(1,𝔽8)⋊C4 | C22×C4 | direct (N × H) |
| 41. C2×C4×C7 | C2×C3×C4 | semidirect |
| 43. C2×Dic7 | C2×C3×C4 | semidirect |
| 51. C2×ΓL(1,𝔽8) | C2×C42 | semidirect |
| 57. C22×C7 | C3×C42 | semidirect |
| 61. C4×C7 | C22×C3×C4 | semidirect |
| 62. Dic7 | C22×C3×C4 | semidirect |
| 70. ΓL(1,𝔽8) | C22×C42 | semidirect |
| 74. C22×C4 | ΓL(1,𝔽8)⋊C4 | direct (N × H) |
| 77. C2×C7 | C2×C3×C42 | semidirect |
| 91. C2×C4 | C2×ΓL(1,𝔽8)⋊C4 | direct (N × H) |
| 93. C7 | C22×C3×C42 | semidirect |
| 97. C22 | C4×ΓL(1,𝔽8)⋊C4 | direct (N × H) |
| 102. C4 | C22×ΓL(1,𝔽8)⋊C4 | direct (N × H) |
| 104. 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×C42 | 7 |