Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
372 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 118 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×Dic3⋊C4 | C2 | semidirect |
| 3. C3×C7×#95 | C2 | semidirect |
| 12. C7×#95 | D3 | semidirect |
| 13. #4676 | C7 | direct (N × H) |
| 30. C2×Dic3⋊C4 | C2×C7 | semidirect |
| 31. C3×#95 | C2×C7 | semidirect |
| 62. #95 | D3×C7 | semidirect |
| 81. C3×C7 | #396 | semidirect |
| 109. C7 | #4676 | direct (N × H) |
| 122. C3 | C7×#396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×(C2×D3)⋊C4 | 2 |
| C2×C7×Dic3⋊C4 | 2 |
| C3×C7×#95 | 2 |
| C7×#396 | 3 |
| #4676 | 7 |