Finite Group DatabasebetaFinite Group Databasebeta← C22×C4×C22⋊ΓL(1,𝔽8) #13062309
Order 1344.
634 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 135 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. C2×C4×C22⋊ΓL(1,𝔽8) | C2 | direct (N × H) |
| 3. C24×C4×C7 | C3 | semidirect |
| 4. C22×C22⋊ΓL(1,𝔽8) | C4 | direct (N × H) |
| 6. C4×C22⋊ΓL(1,𝔽8) | C22 | direct (N × H) |
| 12. C23×C4×C7 | C2×C3 | semidirect |
| 14. C2×C22⋊ΓL(1,𝔽8) | C2×C4 | direct (N × H) |
| 21. C24×C7 | C3×C4 | semidirect |
| 30. C22×C4×C7 | A4 | semidirect |
| 31. C22×C4×C7 | C22×C3 | semidirect |
| 34. C22⋊ΓL(1,𝔽8) | C22×C4 | direct (N × H) |
| 38. C24×C4 | ΓL(1,𝔽8) | semidirect |
| 48. C23×C7 | C2×C3×C4 | semidirect |
| 56. C2×C4×C7 | C2×A4 | semidirect |
| 67. C23×C4 | C2×ΓL(1,𝔽8) | semidirect |
| 77. C22×C7 | C4×A4 | semidirect |
| 78. C22×C7 | C22×C3×C4 | semidirect |
| 81. C4×C7 | C22×A4 | semidirect |
| 90. C24 | C4×ΓL(1,𝔽8) | semidirect |
| 99. C22×C4 | C22×ΓL(1,𝔽8) | semidirect |
| 100. C22×C4 | C22⋊ΓL(1,𝔽8) | direct (N × H) |
| 104. C2×C7 | C2×C4×A4 | semidirect |
| 119. C23 | C2×C4×ΓL(1,𝔽8) | semidirect |
| 127. C2×C4 | C2×C22⋊ΓL(1,𝔽8) | direct (N × H) |
| 128. C7 | C22×C4×A4 | semidirect |
| 140. C22 | C22×C4×ΓL(1,𝔽8) | semidirect |
| 141. C22 | C4×C22⋊ΓL(1,𝔽8) | direct (N × H) |
| 144. C4 | C22×C22⋊ΓL(1,𝔽8) | direct (N × H) |
| 149. C2 | C2×C4×C22⋊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×C22⋊ΓL(1,𝔽8) | 2 |
| C2×C4×C22⋊ΓL(1,𝔽8) | 2 |
| C24×C4×C7 | 3 |
| C22×C4×ΓL(1,𝔽8) | 4 |
| C22×C4×A4 | 7 |