Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 324 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×C7×#127 | C2 | semidirect |
| 2. C2×C7×#213 | C2 | semidirect |
| 3. C7×#874 | C2 | semidirect |
| 4. C4×C7×C3⋊C8 | C2 | semidirect |
| 15. C7×#127 | D3 | semidirect |
| 17. #5073 | C7 | direct (N × H) |
| 26. C7×C3⋊C8 | D4 | semidirect |
| 34. C3×#127 | C2×C7 | semidirect |
| 35. C2×#213 | C2×C7 | semidirect |
| 36. #874 | C2×C7 | semidirect |
| 37. C4×C3⋊C8 | C2×C7 | semidirect |
| 43. C3×C4×C7 | D8 | semidirect |
| 68. #127 | D3×C7 | semidirect |
| 75. C4×C7 | #213 | semidirect |
| 85. C3⋊C8 | C7×D4 | semidirect |
| 86. C3×C7 | #493 | semidirect |
| 103. C3×C4 | C7×D8 | semidirect |
| 114. C7 | #5073 | direct (N × H) |
| 124. C4 | C7×#213 | semidirect |
| 126. C3 | C7×#493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#127 | 2 |
| C2×C7×#213 | 2 |
| C7×#874 | 2 |
| C4×C7×C3⋊C8 | 2 |
| C7×#493 | 3 |
| #5073 | 7 |