Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
388 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 5. C4×C7×C4⋊C4 | C3 | semidirect |
| 10. C4⋊C4×ΓL(1,𝔽8) | C4 | direct (N × H) |
| 12. C42×ΓL(1,𝔽8) | C4 | semidirect |
| 33. C7×C4⋊C4 | C3×C4 | semidirect |
| 35. C42×C7 | C3×C4 | semidirect |
| 47. C4×ΓL(1,𝔽8) | C42 | semidirect |
| 48. C4×ΓL(1,𝔽8) | C4⋊C4 | direct (N × H) |
| 49. C4×C4⋊C4 | ΓL(1,𝔽8) | direct (N × H) |
| 84. C4×C7 | C3×C42 | semidirect |
| 85. C4×C7 | C3×C4⋊C4 | semidirect |
| 97. ΓL(1,𝔽8) | C4×C4⋊C4 | direct (N × H) |
| 102. C4⋊C4 | C4×ΓL(1,𝔽8) | direct (N × H) |
| 104. C42 | C4×ΓL(1,𝔽8) | semidirect |
| 130. C7 | C3×C4×C4⋊C4 | semidirect |
| 143. C4 | C42×ΓL(1,𝔽8) | semidirect |
| 144. C4 | C4⋊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 |
|---|---|
| C2×C4⋊C4×ΓL(1,𝔽8) | 2 |
| C2×C42×ΓL(1,𝔽8) | 2 |
| ΓL(1,𝔽8)×#95 | 2 |
| C4×C7×C4⋊C4 | 3 |
| C3×C4×C4⋊C4 | 7 |