Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 91 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. C4×D84 | C2 | semidirect |
| 3. C3×C4×C7×C8 | C2 | semidirect |
| 4. #10620660 | C2 | semidirect |
| 5. #10620657 | C2 | semidirect |
| 14. D168 | C4 | direct (N × H) |
| 17. C4×C7×C8 | D3 | semidirect |
| 27. D84 | C2×C4 | semidirect |
| 30. C3×C7×C8 | C2×C4 | semidirect |
| 41. C3×C4×C8 | D7 | semidirect |
| 49. C3×C4×C7 | D8 | semidirect |
| 63. C7×C8 | C4×D3 | semidirect |
| 80. C4×C8 | D21 | semidirect |
| 86. C4×C7 | D24 | semidirect |
| 99. C3×C8 | C4×D7 | semidirect |
| 100. C3×C7 | C4×D8 | semidirect |
| 118. C3×C4 | D56 | semidirect |
| 131. C8 | C4×D21 | semidirect |
| 132. C7 | C4×D24 | semidirect |
| 143. C4 | D168 | direct (N × H) |
| 146. C3 | C4×D56 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D168 | 2 |
| C4×D84 | 2 |
| C3×C4×C7×C8 | 2 |
| #10620660 | 2 |
| #10620657 | 2 |
| C4×D56 | 3 |
| C4×D24 | 7 |