Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 110 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. C3×C4×C7×D4 | C2 | semidirect |
| 3. C4×C7×D12 | C2 | semidirect |
| 4. C7×#832 | C2 | semidirect |
| 5. C7×#809 | C2 | semidirect |
| 6. C7×#807 | C2 | semidirect |
| 7. C4×C7×C3⋊C8 | C2 | semidirect |
| 16. C7×#213 | C4 | direct (N × H) |
| 23. C4×C7×D4 | D3 | semidirect |
| 28. C4×#213 | C7 | direct (N × H) |
| 32. C3×C7×D4 | C2×C4 | semidirect |
| 40. C7×D12 | C2×C4 | semidirect |
| 43. C7×C3⋊C8 | C2×C4 | semidirect |
| 56. C3×C4×D4 | C2×C7 | semidirect |
| 58. C4×D12 | C2×C7 | semidirect |
| 59. #832 | C2×C7 | semidirect |
| 60. #809 | C2×C7 | semidirect |
| 61. #807 | C2×C7 | semidirect |
| 62. C4×C3⋊C8 | C2×C7 | semidirect |
| 72. C3×C4×C7 | D8 | semidirect |
| 82. C7×D4 | C4×D3 | semidirect |
| 99. #213 | C4×C7 | direct (N × H) |
| 111. C4×D4 | D3×C7 | semidirect |
| 126. C4×C7 | #213 | direct (N × H) |
| 132. C3×D4 | C2×C4×C7 | semidirect |
| 140. D12 | C2×C4×C7 | semidirect |
| 143. C3⋊C8 | C2×C4×C7 | semidirect |
| 144. C3×C7 | C4×D8 | semidirect |
| 171. C3×C4 | C7×D8 | semidirect |
| 180. D4 | C4×D3×C7 | semidirect |
| 190. C7 | C4×#213 | direct (N × H) |
| 206. C4 | C7×#213 | direct (N × H) |
| 209. C3 | C4×C7×D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C7×D4 | 2 |
| C2×C7×#213 | 2 |
| C4×C7×D12 | 2 |
| C7×#832 | 2 |
| C7×#809 | 2 |
| C7×#807 | 2 |
| C4×C7×C3⋊C8 | 2 |
| C4×C7×D8 | 3 |
| C4×#213 | 7 |