Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
168 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 168 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 |
|---|---|---|
| 2. C3×C7×M32 | C2 | semidirect |
| 3. C2×C7×C3⋊C16 | C2 | semidirect |
| 4. C7×#798 | C2 | semidirect |
| 5. D3×C7×C16 | C2 | semidirect |
| 17. C7×M32 | D3 | semidirect |
| 20. #4907 | C7 | direct (N × H) |
| 38. C3×M32 | C2×C7 | semidirect |
| 39. C2×C3⋊C16 | C2×C7 | semidirect |
| 40. #798 | C2×C7 | semidirect |
| 41. D3×C16 | C2×C7 | semidirect |
| 69. M32 | D3×C7 | semidirect |
| 85. C3×C7 | #504 | semidirect |
| 110. C7 | #4907 | direct (N × H) |
| 119. C3 | C7×#504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#901 | 2 |
| C3×C7×M32 | 2 |
| C2×C7×C3⋊C16 | 2 |
| C7×#798 | 2 |
| D3×C7×C16 | 2 |
| C7×#504 | 3 |
| #4907 | 7 |