Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
276 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 171 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. ΓL(1,𝔽8)×C4⋊C8 | C2 | direct (N × H) |
| 4. C2×C7×C4⋊C8 | C3 | semidirect |
| 14. C7×C4⋊C8 | C2×C3 | semidirect |
| 18. C2×C4×ΓL(1,𝔽8) | C8 | semidirect |
| 42. C4×ΓL(1,𝔽8) | C2×C8 | semidirect |
| 45. C2×C4⋊C8 | ΓL(1,𝔽8) | direct (N × H) |
| 48. C2×C4×C7 | C3×C8 | semidirect |
| 63. C2×ΓL(1,𝔽8) | C4⋊C8 | direct (N × H) |
| 69. C4⋊C8 | C2×ΓL(1,𝔽8) | direct (N × H) |
| 76. C4×C7 | C2×C3×C8 | semidirect |
| 89. ΓL(1,𝔽8) | C2×C4⋊C8 | direct (N × H) |
| 97. C2×C7 | C3×C4⋊C8 | semidirect |
| 112. C2×C4 | C8×ΓL(1,𝔽8) | semidirect |
| 120. C7 | C2×C3×C4⋊C8 | semidirect |
| 131. C4 | C2×C8×ΓL(1,𝔽8) | semidirect |
| 135. C2 | ΓL(1,𝔽8)×C4⋊C8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×ΓL(1,𝔽8) | 2 |
| C2×C42×ΓL(1,𝔽8) | 2 |
| ΓL(1,𝔽8)×C4⋊C8 | 2 |
| C2×C7×C4⋊C8 | 3 |
| C2×C3×C4⋊C8 | 7 |