Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. C2×C8×D21 | C2 | semidirect |
| 3. C3×C4×C7×C8 | C2 | semidirect |
| 4. #10620659 | C2 | semidirect |
| 5. C4⋊(C3⋊(C7⋊C8)) | C2 | semidirect |
| 18. C4×C7×C8 | D3 | semidirect |
| 27. D84 | C8 | direct (N × H) |
| 31. C3×C7×C8 | D4 | semidirect |
| 44. C3×C4×C8 | D7 | semidirect |
| 50. C2×D21 | C2×C8 | semidirect |
| 52. C3×C4×C7 | C2×C8 | semidirect |
| 66. C7×C8 | D12 | semidirect |
| 85. C4×C8 | D21 | semidirect |
| 91. C4×C7 | D3×C8 | semidirect |
| 104. C3×C8 | D28 | semidirect |
| 106. C3×C7 | C8×D4 | semidirect |
| 125. C3×C4 | C8×D7 | semidirect |
| 139. C8 | D84 | direct (N × H) |
| 140. C7 | C8×D12 | semidirect |
| 151. C4 | C8×D21 | semidirect |
| 154. C3 | C8×D28 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D21 | 2 |
| C4×D84 | 2 |
| C3×C4×C7×C8 | 2 |
| #10620659 | 2 |
| C4⋊(C3⋊(C7⋊C8)) | 2 |
| C8×D28 | 3 |
| C8×D12 | 7 |