Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
660 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 254 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. C22×C3×C7×Q8 | C2 | semidirect |
| 3. C7×#947 | C2 | direct (N × H) |
| 4. C2×C7×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C2×C4×C7×Dic3 | C2 | semidirect |
| 9. C2×C3×C7×Q8 | C22 | semidirect |
| 15. C7×(C2×D3)⋊C4 | C22 | semidirect |
| 16. C4×C7×Dic3 | C22 | semidirect |
| 17. C22×C7×Q8 | D3 | semidirect |
| 22. C2×#947 | C7 | direct (N × H) |
| 37. C2×C7×Q8 | C2×D3 | semidirect |
| 45. C22×C3×Q8 | C2×C7 | semidirect |
| 47. #947 | C2×C7 | direct (N × H) |
| 48. C2×(C2×D3)⋊C4 | C2×C7 | semidirect |
| 49. C2×C4×Dic3 | C2×C7 | semidirect |
| 74. C2×C3×Q8 | C22×C7 | semidirect |
| 80. (C2×D3)⋊C4 | C22×C7 | semidirect |
| 81. C4×Dic3 | C22×C7 | semidirect |
| 82. C2×C3×C7 | #124 | semidirect |
| 86. C22×Q8 | D3×C7 | semidirect |
| 112. C3×C7 | C2×#124 | semidirect |
| 115. C2×Q8 | C2×D3×C7 | semidirect |
| 124. C2×C7 | #947 | direct (N × H) |
| 148. C7 | C2×#947 | direct (N × H) |
| 149. C2×C3 | C7×#124 | semidirect |
| 162. C3 | C2×C7×#124 | semidirect |
| 164. C2 | C7×#947 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C7×Q8 | 2 |
| C22×C7×D12 | 2 |
| C7×#947 | 2 |
| C2×C7×(C2×D3)⋊C4 | 2 |
| C2×C4×C7×Dic3 | 2 |
| C2×C7×#124 | 3 |
| C2×#947 | 7 |