Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
180 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 142 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. C7×#812 | C2 | direct (N × H) |
| 3. C2×C7×C3⋊C16 | C2 | semidirect |
| 10. C7×C3⋊C16 | C22 | semidirect |
| 14. C2×#812 | C7 | direct (N × H) |
| 30. #812 | C2×C7 | direct (N × H) |
| 31. C2×C3⋊C16 | C2×C7 | semidirect |
| 52. C3⋊C16 | C22×C7 | semidirect |
| 54. C2×C3×C7 | M32 | semidirect |
| 73. C3×C7 | C2×M32 | semidirect |
| 81. C2×C7 | #812 | direct (N × H) |
| 97. C7 | C2×#812 | direct (N × H) |
| 99. C2×C3 | C7×M32 | semidirect |
| 107. C3 | C2×C7×M32 | semidirect |
| 109. C2 | C7×#812 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C7×C8 | 2 |
| C7×#812 | 2 |
| C2×C7×C3⋊C16 | 2 |
| C2×C7×M32 | 3 |
| C2×#812 | 7 |