Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
516 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 192 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 | semidirect |
| 4. ΓL(1,𝔽8)⋊#95 | C2 | semidirect |
| 5. C4×C22⋊Dic7 | C3 | semidirect |
| 8. C22×C4×ΓL(1,𝔽8) | C4 | semidirect |
| 12. (C22⋊Dic7)⋊C3 | C4 | direct (N × H) |
| 16. C2×C4×Dic7 | C2×C3 | semidirect |
| 17. C7⋊#95 | C2×C3 | semidirect |
| 31. C2×ΓL(1,𝔽8)⋊C4 | C2×C4 | semidirect |
| 34. C22×C4×C7 | C3×C4 | semidirect |
| 38. C22⋊Dic7 | C3×C4 | semidirect |
| 47. C22×ΓL(1,𝔽8) | C42 | semidirect |
| 53. C4×ΓL(1,𝔽8) | C22⋊C4 | semidirect |
| 68. C2×Dic7 | C2×C3×C4 | semidirect |
| 89. C22×C7 | C3×C42 | semidirect |
| 95. C4×C7 | C3×C22⋊C4 | semidirect |
| 110. ΓL(1,𝔽8) | C4×C22⋊C4 | semidirect |
| 114. C22×C4 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 148. C7 | C3×C4×C22⋊C4 | semidirect |
| 157. C22 | C4×ΓL(1,𝔽8)⋊C4 | semidirect |
| 164. C4 | (C22⋊Dic7)⋊C3 | 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 |
| C2×(C22⋊Dic7)⋊C3 | 2 |
| C2×C4×ΓL(1,𝔽8)⋊C4 | 2 |
| ΓL(1,𝔽8)⋊#95 | 2 |
| C4×C22⋊Dic7 | 3 |
| C3×C4×C22⋊C4 | 7 |