Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
596 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 596 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 |
|---|---|---|
| 2. C22×C3×Dic14 | C2 | semidirect |
| 3. C22×C3⋊(C7⋊C8) | C2 | semidirect |
| 4. C2×#66564 | C2 | direct (N × H) |
| 12. C2×C3×Dic14 | C22 | semidirect |
| 13. C2×C3⋊(C7⋊C8) | C22 | semidirect |
| 14. #66564 | C22 | direct (N × H) |
| 16. C22×Dic14 | D3 | semidirect |
| 29. C3×Dic14 | C23 | semidirect |
| 30. C3⋊(C7⋊C8) | C23 | semidirect |
| 37. C2×Dic14 | C2×D3 | semidirect |
| 44. C22×C3×C7 | SD16 | semidirect |
| 61. Dic14 | C22×D3 | semidirect |
| 72. C2×C3×C7 | C2×SD16 | semidirect |
| 81. C22×C7 | #215 | semidirect |
| 97. C3×C7 | C22×SD16 | semidirect |
| 108. C2×C7 | C2×#215 | semidirect |
| 110. C22×C3 | #1142 | semidirect |
| 128. C7 | C22×#215 | semidirect |
| 129. C2×C3 | C2×#1142 | semidirect |
| 134. C22 | #66564 | direct (N × H) |
| 139. C3 | C22×#1142 | semidirect |
| 141. C2 | C2×#66564 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D12 | 2 |
| C22×C3×Dic14 | 2 |
| C22×C3⋊(C7⋊C8) | 2 |
| C2×#66564 | 2 |
| C22×#1142 | 3 |
| C22×#215 | 7 |