Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
244 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 122 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×C7×#208 | C2 | semidirect |
| 3. C7×#830 | C2 | semidirect |
| 4. C7×C4⋊(C3⋊C8) | C2 | semidirect |
| 5. C4×C7×C3⋊C8 | C2 | semidirect |
| 21. #5012 | C7 | direct (N × H) |
| 32. C7×C3⋊C8 | D4 | semidirect |
| 43. C2×#208 | C2×C7 | semidirect |
| 44. #830 | C2×C7 | semidirect |
| 45. C4⋊(C3⋊C8) | C2×C7 | semidirect |
| 46. C4×C3⋊C8 | C2×C7 | semidirect |
| 53. C3×C4×C7 | M16 | semidirect |
| 92. C4×C7 | #208 | semidirect |
| 105. C3⋊C8 | C7×D4 | semidirect |
| 106. C3×C7 | #436 | semidirect |
| 126. C3×C4 | C7×M16 | semidirect |
| 140. C7 | #5012 | direct (N × H) |
| 151. C4 | C7×#208 | semidirect |
| 154. C3 | C7×#436 | 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×#208 | 2 |
| C7×#830 | 2 |
| C7×C4⋊(C3⋊C8) | 2 |
| C4×C7×C3⋊C8 | 2 |
| C7×#436 | 3 |
| #5012 | 7 |