Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
196 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 64 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. C2×D168 | C2 | semidirect |
| 2. C2×C3×D56 | C2 | semidirect |
| 3. C2×C7×C3⋊C16 | C2 | semidirect |
| 4. #10620473 | C2 | direct (N × H) |
| 10. D168 | C22 | semidirect |
| 12. C3×D56 | C22 | semidirect |
| 13. C7×C3⋊C16 | C22 | semidirect |
| 15. C2×D56 | D3 | semidirect |
| 34. D56 | C2×D3 | semidirect |
| 39. C2×C3⋊C16 | D7 | semidirect |
| 64. C3⋊C16 | C2×D7 | semidirect |
| 65. C2×C3×C7 | D16 | semidirect |
| 89. C3×C7 | C2×D16 | semidirect |
| 98. C2×C7 | #826 | semidirect |
| 118. C7 | C2×#826 | semidirect |
| 120. C2×C3 | D112 | semidirect |
| 130. C3 | C2×D112 | semidirect |
| 133. C2 | #10620473 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D168 | 2 |
| C2×C3×D56 | 2 |
| C2×C7×C3⋊C16 | 2 |
| #10620473 | 2 |
| C2×D112 | 3 |
| C2×#826 | 7 |