Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
676 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 192 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. C22×D84 | C2 | semidirect |
| 2. C22×C3×D28 | C2 | semidirect |
| 3. C22×C7×C3⋊C8 | C2 | semidirect |
| 4. C2×#66561 | C2 | direct (N × H) |
| 10. C2×D84 | C22 | semidirect |
| 12. C2×C3×D28 | C22 | semidirect |
| 13. C2×C7×C3⋊C8 | C22 | semidirect |
| 14. #66561 | C22 | direct (N × H) |
| 16. C22×D28 | D3 | semidirect |
| 28. D84 | C23 | semidirect |
| 30. C3×D28 | C23 | semidirect |
| 31. C7×C3⋊C8 | C23 | semidirect |
| 38. C2×D28 | C2×D3 | semidirect |
| 44. C22×C3⋊C8 | D7 | semidirect |
| 45. C22×C3×C7 | D8 | semidirect |
| 64. D28 | C22×D3 | semidirect |
| 74. C2×C3⋊C8 | C2×D7 | semidirect |
| 75. C2×C3×C7 | C2×D8 | semidirect |
| 83. C22×C7 | #213 | semidirect |
| 102. C3⋊C8 | C22×D7 | semidirect |
| 103. C3×C7 | C22×D8 | semidirect |
| 113. C2×C7 | C2×#213 | semidirect |
| 119. C22×C3 | D56 | semidirect |
| 137. C7 | C22×#213 | semidirect |
| 139. C2×C3 | C2×D56 | semidirect |
| 146. C22 | #66561 | direct (N × H) |
| 150. C3 | C22×D56 | semidirect |
| 153. C2 | C2×#66561 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D84 | 2 |
| C22×C3×D28 | 2 |
| C22×C7×C3⋊C8 | 2 |
| C2×#66561 | 2 |
| C22×D56 | 3 |
| C22×#213 | 7 |