Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 102 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×Q8 | C2 | semidirect |
| 4. C7×#835 | C2 | semidirect |
| 6. C7×#807 | C2 | semidirect |
| 7. C7×#803 | C2 | semidirect |
| 16. C7×#215 | C4 | semidirect |
| 22. C4×C7×Q8 | D3 | semidirect |
| 28. #5026 | C7 | direct (N × H) |
| 31. C3×C7×Q8 | C2×C4 | semidirect |
| 42. C7×C3⋊C8 | C2×C4 | semidirect |
| 55. C3×C4×Q8 | C2×C7 | semidirect |
| 58. #835 | C2×C7 | semidirect |
| 60. #807 | C2×C7 | semidirect |
| 61. #803 | C2×C7 | semidirect |
| 76. C7×Q8 | C4×D3 | semidirect |
| 95. #215 | C4×C7 | semidirect |
| 105. C4×Q8 | D3×C7 | semidirect |
| 124. C3×Q8 | C2×C4×C7 | semidirect |
| 135. C3⋊C8 | C2×C4×C7 | semidirect |
| 136. C3×C7 | #440 | semidirect |
| 166. Q8 | C4×D3×C7 | semidirect |
| 178. C7 | #5026 | direct (N × H) |
| 194. C3 | C7×#440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C7×Q8 | 2 |
| C2×C7×#215 | 2 |
| C4×C7×D12 | 2 |
| C7×#835 | 2 |
| C7×#809 | 2 |
| C7×#807 | 2 |
| C7×#803 | 2 |
| C7×#440 | 3 |
| #5026 | 7 |