Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
256 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 94 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. C3×C4×C7×Q8 | C2 | semidirect |
| 2. C2×C7×#215 | C2 | semidirect |
| 4. C7×#809 | C2 | semidirect |
| 5. C7×C4⋊(C3⋊C8) | C2 | semidirect |
| 19. C4×C7×Q8 | D3 | semidirect |
| 22. #5027 | C7 | direct (N × H) |
| 25. C3×C7×Q8 | D4 | semidirect |
| 46. C3×C4×Q8 | C2×C7 | semidirect |
| 47. C2×#215 | C2×C7 | semidirect |
| 49. #809 | C2×C7 | semidirect |
| 50. C4⋊(C3⋊C8) | C2×C7 | semidirect |
| 58. C3×C4×C7 | SD16 | semidirect |
| 64. C7×Q8 | D12 | semidirect |
| 91. C4×Q8 | D3×C7 | semidirect |
| 101. C4×C7 | #215 | semidirect |
| 106. C3×Q8 | C7×D4 | semidirect |
| 117. C3×C7 | #460 | semidirect |
| 139. C3×C4 | C7×SD16 | semidirect |
| 144. Q8 | C7×D12 | semidirect |
| 155. C7 | #5027 | direct (N × H) |
| 167. C4 | C7×#215 | semidirect |
| 170. C3 | C7×#460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C7×Q8 | 2 |
| C2×C7×#215 | 2 |
| C7×#874 | 2 |
| C7×#809 | 2 |
| C7×C4⋊(C3⋊C8) | 2 |
| C7×#460 | 3 |
| #5027 | 7 |