Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
516 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 175 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×C3×C42×C7 | C2 | semidirect |
| 4. C2×C4×Dic21 | C2 | semidirect |
| 5. #10620670 | C2 | semidirect |
| 14. C2×C4×D21 | C4 | semidirect |
| 16. #66631 | C4 | direct (N × H) |
| 19. C2×C42×C7 | D3 | semidirect |
| 33. C2×C3×C4×C7 | C2×C4 | semidirect |
| 41. C2×Dic21 | C2×C4 | semidirect |
| 55. C2×C3×C42 | D7 | semidirect |
| 68. C2×D21 | C42 | semidirect |
| 70. C3×C4×C7 | C22⋊C4 | semidirect |
| 83. C2×C4×C7 | C4×D3 | semidirect |
| 113. C2×C42 | D21 | semidirect |
| 126. C4×C7 | (C2×D3)⋊C4 | semidirect |
| 138. C2×C3×C4 | C4×D7 | semidirect |
| 148. C3×C7 | C4×C22⋊C4 | semidirect |
| 177. C3×C4 | (C2×D7)⋊C4 | semidirect |
| 196. C2×C4 | C4×D21 | semidirect |
| 199. C7 | C4×(C2×D3)⋊C4 | semidirect |
| 219. C4 | #66631 | direct (N × H) |
| 220. C3 | C4×(C2×D7)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D21 | 2 |
| C2×C3×C42×C7 | 2 |
| C2×#66631 | 2 |
| C2×C4×Dic21 | 2 |
| #10620670 | 2 |
| C4×(C2×D7)⋊C4 | 3 |
| C4×(C2×D3)⋊C4 | 7 |