Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
596 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 254 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. C2×C3×#1142 | C2 | direct (N × H) |
| 4. C22×C3×C7⋊C8 | C2 | semidirect |
| 5. C22×#1142 | C3 | direct (N × H) |
| 12. C2×C3×Dic14 | C22 | semidirect |
| 13. C3×#1142 | C22 | direct (N × H) |
| 14. C2×C3×C7⋊C8 | C22 | semidirect |
| 16. C22×Dic14 | C2×C3 | semidirect |
| 17. C2×#1142 | C2×C3 | direct (N × H) |
| 18. C22×C7⋊C8 | C2×C3 | semidirect |
| 29. C3×Dic14 | C23 | semidirect |
| 30. C3×C7⋊C8 | C23 | semidirect |
| 37. C2×Dic14 | C22×C3 | semidirect |
| 38. #1142 | C22×C3 | direct (N × H) |
| 39. C2×C7⋊C8 | C22×C3 | semidirect |
| 46. C22×C3×C7 | SD16 | semidirect |
| 61. Dic14 | C23×C3 | semidirect |
| 62. C7⋊C8 | C23×C3 | semidirect |
| 73. C2×C3×C7 | C2×SD16 | semidirect |
| 81. C22×C7 | C3×SD16 | semidirect |
| 97. C3×C7 | C22×SD16 | semidirect |
| 108. C2×C7 | C2×C3×SD16 | semidirect |
| 112. C22×C3 | #1142 | direct (N × H) |
| 128. C7 | C22×C3×SD16 | semidirect |
| 130. C2×C3 | C2×#1142 | direct (N × H) |
| 134. C22 | C3×#1142 | direct (N × H) |
| 139. C3 | C22×#1142 | direct (N × H) |
| 141. C2 | C2×C3×#1142 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C7×D4 | 2 |
| C22×C3×Dic14 | 2 |
| C2×C3×#1142 | 2 |
| C22×C3×C7⋊C8 | 2 |
| C22×#1142 | 3 |
| C22×C3×SD16 | 7 |