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 |
|---|---|---|
| 1. C22×C3×C7×Q8 | C2 | semidirect |
| 3. C2×C7×#215 | C2 | direct (N × H) |
| 4. C22×C7×C3⋊C8 | C2 | semidirect |
| 8. C2×C3×C7×Q8 | C22 | semidirect |
| 13. C7×#215 | C22 | direct (N × H) |
| 14. C2×C7×C3⋊C8 | C22 | semidirect |
| 15. C22×C7×Q8 | D3 | semidirect |
| 19. C22×#215 | C7 | direct (N × H) |
| 24. C3×C7×Q8 | C23 | semidirect |
| 30. C7×C3⋊C8 | C23 | semidirect |
| 33. C2×C7×Q8 | C2×D3 | semidirect |
| 40. C22×C3×Q8 | C2×C7 | semidirect |
| 42. C2×#215 | C2×C7 | direct (N × H) |
| 43. C22×C3⋊C8 | C2×C7 | semidirect |
| 44. C22×C3×C7 | SD16 | semidirect |
| 56. C7×Q8 | C22×D3 | semidirect |
| 65. C2×C3×Q8 | C22×C7 | semidirect |
| 70. #215 | C22×C7 | direct (N × H) |
| 71. C2×C3⋊C8 | C22×C7 | semidirect |
| 72. C2×C3×C7 | C2×SD16 | semidirect |
| 75. C22×Q8 | D3×C7 | semidirect |
| 81. C22×C7 | #215 | direct (N × H) |
| 90. C3×Q8 | C23×C7 | semidirect |
| 96. C3⋊C8 | C23×C7 | semidirect |
| 97. C3×C7 | C22×SD16 | semidirect |
| 100. C2×Q8 | C2×D3×C7 | semidirect |
| 108. C2×C7 | C2×#215 | direct (N × H) |
| 110. C22×C3 | C7×SD16 | semidirect |
| 121. Q8 | C22×D3×C7 | semidirect |
| 128. C7 | C22×#215 | direct (N × H) |
| 129. C2×C3 | C2×C7×SD16 | semidirect |
| 134. C22 | C7×#215 | direct (N × H) |
| 139. C3 | C22×C7×SD16 | semidirect |
| 141. C2 | C2×C7×#215 | 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×Q8 | 2 |
| C22×C7×D12 | 2 |
| C2×C7×#215 | 2 |
| C22×C7×C3⋊C8 | 2 |
| C22×C7×SD16 | 3 |
| C22×#215 | 7 |