Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
1348 conjugacy classes of subgroups; only the 574 normal subgroups are shown.
This group has 1348 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 |
|---|---|---|
| 2. C23×C7×Dic3 | C2 | semidirect |
| 3. C2×C7×#217 | C2 | direct (N × H) |
| 6. C24×C3×C7 | C4 | semidirect |
| 10. C22×C7×Dic3 | C22 | semidirect |
| 11. C7×#217 | C22 | direct (N × H) |
| 15. C22×#217 | C7 | direct (N × H) |
| 19. C23×C3×C7 | C2×C4 | semidirect |
| 24. C2×C7×Dic3 | C23 | semidirect |
| 26. C24×C7 | Dic3 | semidirect |
| 33. C23×Dic3 | C2×C7 | semidirect |
| 34. C2×#217 | C2×C7 | direct (N × H) |
| 37. C22×C3×C7 | C22⋊C4 | semidirect |
| 39. C22×C3×C7 | C22×C4 | semidirect |
| 47. C23×C7 | C2×Dic3 | semidirect |
| 54. C24×C3 | C4×C7 | semidirect |
| 58. C22×Dic3 | C22×C7 | semidirect |
| 59. #217 | C22×C7 | direct (N × H) |
| 61. C2×C3×C7 | C2×C22⋊C4 | semidirect |
| 69. C22×C7 | #217 | direct (N × H) |
| 71. C22×C7 | C22×Dic3 | semidirect |
| 78. C23×C3 | C2×C4×C7 | semidirect |
| 83. C2×Dic3 | C23×C7 | semidirect |
| 84. C3×C7 | C22×C22⋊C4 | semidirect |
| 86. C24 | C7×Dic3 | semidirect |
| 93. C2×C7 | C2×#217 | direct (N × H) |
| 98. C22×C3 | C7×C22⋊C4 | semidirect |
| 100. C22×C3 | C22×C4×C7 | semidirect |
| 107. C23 | C2×C7×Dic3 | semidirect |
| 113. C7 | C22×#217 | direct (N × H) |
| 115. C2×C3 | C2×C7×C22⋊C4 | semidirect |
| 120. C22 | C7×#217 | direct (N × H) |
| 122. C22 | C22×C7×Dic3 | semidirect |
| 126. C3 | C22×C7×C22⋊C4 | semidirect |
| 128. C2 | C2×C7×#217 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C3×C7 | 2 |
| C23×C7×Dic3 | 2 |
| C2×C7×#217 | 2 |
| C22×C7×C22⋊C4 | 3 |
| C22×#217 | 7 |