Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
836 conjugacy classes of subgroups; only the 574 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 574 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 |
|---|---|---|
| 3. C2×C7×C4⋊Dic3 | C2 | direct (N × H) |
| 6. C22×C3×C4×C7 | C4 | semidirect |
| 10. C7×C4⋊Dic3 | C22 | direct (N × H) |
| 14. C22×C4⋊Dic3 | C7 | direct (N × H) |
| 19. C2×C3×C4×C7 | C2×C4 | semidirect |
| 26. C22×C4×C7 | Dic3 | semidirect |
| 31. C2×C4⋊Dic3 | C2×C7 | direct (N × H) |
| 32. C22×C3×C7 | C4⋊C4 | semidirect |
| 37. C3×C4×C7 | C22×C4 | semidirect |
| 46. C2×C4×C7 | C2×Dic3 | semidirect |
| 49. C22×C3×C4 | C4×C7 | semidirect |
| 53. C4⋊Dic3 | C22×C7 | direct (N × H) |
| 54. C2×C3×C7 | C2×C4⋊C4 | semidirect |
| 61. C22×C7 | C4⋊Dic3 | direct (N × H) |
| 67. C4×C7 | C22×Dic3 | semidirect |
| 72. C2×C3×C4 | C2×C4×C7 | semidirect |
| 76. C3×C7 | C22×C4⋊C4 | semidirect |
| 80. C22×C4 | C7×Dic3 | semidirect |
| 83. C2×C7 | C2×C4⋊Dic3 | direct (N × H) |
| 87. C22×C3 | C7×C4⋊C4 | semidirect |
| 92. C3×C4 | C22×C4×C7 | semidirect |
| 100. C2×C4 | C2×C7×Dic3 | semidirect |
| 102. C7 | C22×C4⋊Dic3 | direct (N × H) |
| 103. C2×C3 | C2×C7×C4⋊C4 | semidirect |
| 107. C22 | C7×C4⋊Dic3 | direct (N × H) |
| 113. C4 | C22×C7×Dic3 | semidirect |
| 114. C3 | C22×C7×C4⋊C4 | semidirect |
| 115. C2 | C2×C7×C4⋊Dic3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C4×C7 | 2 |
| C23×C7×Dic3 | 2 |
| C2×C7×C4⋊Dic3 | 2 |
| C22×C7×C4⋊C4 | 3 |
| C22×C4⋊Dic3 | 7 |