Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
380 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 126 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. C3×C7×#117 | C2 | semidirect |
| 3. C2×C7×#208 | C2 | semidirect |
| 4. C7×#809 | C2 | semidirect |
| 10. C2×C7×D12 | C4 | semidirect |
| 12. C3×C7×C4⋊C4 | C22 | semidirect |
| 16. C2×C7×C3⋊C8 | C22 | semidirect |
| 19. C7×#117 | D3 | semidirect |
| 21. #5001 | C7 | direct (N × H) |
| 43. C7×C4⋊C4 | C2×D3 | semidirect |
| 47. C3×#117 | C2×C7 | semidirect |
| 48. C2×#208 | C2×C7 | semidirect |
| 49. #809 | C2×C7 | semidirect |
| 78. C2×D12 | C4×C7 | semidirect |
| 80. C3×C4⋊C4 | C22×C7 | semidirect |
| 84. C2×C3⋊C8 | C22×C7 | semidirect |
| 91. #117 | D3×C7 | semidirect |
| 116. C3×C7 | #418 | semidirect |
| 125. C4⋊C4 | C2×D3×C7 | semidirect |
| 155. C7 | #5001 | direct (N × H) |
| 170. C3 | C7×#418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D12 | 2 |
| C3×C7×#117 | 2 |
| C2×C7×#208 | 2 |
| C7×#809 | 2 |
| C7×#418 | 3 |
| #5001 | 7 |