Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
404 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 158 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 |
|---|---|---|
| 2. C2×C3×C7×C4⋊C4 | C2 | semidirect |
| 3. C22×C7×C3⋊C8 | C2 | semidirect |
| 4. C7×#809 | C2 | direct (N × H) |
| 11. C2×C7×D12 | C4 | semidirect |
| 14. C3×C7×C4⋊C4 | C22 | semidirect |
| 16. C2×C7×C3⋊C8 | C22 | semidirect |
| 19. C2×C7×C4⋊C4 | D3 | semidirect |
| 21. C2×#809 | C7 | direct (N × H) |
| 35. C7×D12 | C2×C4 | semidirect |
| 47. C7×C4⋊C4 | C2×D3 | semidirect |
| 49. C2×C3×C4⋊C4 | C2×C7 | semidirect |
| 50. C22×C3⋊C8 | C2×C7 | semidirect |
| 51. #809 | C2×C7 | direct (N × H) |
| 85. C2×D12 | C4×C7 | semidirect |
| 88. C3×C4⋊C4 | C22×C7 | semidirect |
| 90. C2×C3⋊C8 | C22×C7 | semidirect |
| 91. C2×C3×C7 | #102 | semidirect |
| 98. C2×C4⋊C4 | D3×C7 | semidirect |
| 125. D12 | C2×C4×C7 | semidirect |
| 127. C3×C7 | C2×#102 | semidirect |
| 138. C4⋊C4 | C2×D3×C7 | semidirect |
| 140. C2×C7 | #809 | direct (N × H) |
| 171. C7 | C2×#809 | direct (N × H) |
| 172. C2×C3 | C7×#102 | semidirect |
| 189. C3 | C2×C7×#102 | semidirect |
| 191. C2 | C7×#809 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D12 | 2 |
| C2×C3×C7×C4⋊C4 | 2 |
| C22×C7×C3⋊C8 | 2 |
| C7×#809 | 2 |
| C2×C7×#102 | 3 |
| C2×#809 | 7 |