Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 90 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×C7×C4⋊Q8 | C2 | semidirect |
| 4. C7×#835 | C2 | semidirect |
| 5. C7×C4⋊(C3⋊C8) | C2 | semidirect |
| 18. C7×C4⋊Q8 | D3 | semidirect |
| 22. #5083 | C7 | direct (N × H) |
| 45. C3×C4⋊Q8 | C2×C7 | semidirect |
| 48. #835 | C2×C7 | semidirect |
| 49. C4⋊(C3⋊C8) | C2×C7 | semidirect |
| 56. C3×C4×C7 | SD16 | semidirect |
| 88. C4⋊Q8 | D3×C7 | semidirect |
| 99. C4×C7 | #215 | semidirect |
| 114. C3×C7 | #461 | semidirect |
| 135. C3×C4 | C7×SD16 | semidirect |
| 151. C7 | #5083 | direct (N × H) |
| 163. C4 | C7×#215 | semidirect |
| 166. C3 | C7×#461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×C4⋊Q8 | 2 |
| C2×C7×#215 | 2 |
| C4×C7×D12 | 2 |
| C7×#835 | 2 |
| C7×C4⋊(C3⋊C8) | 2 |
| C7×#461 | 3 |
| #5083 | 7 |