Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
380 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 126 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. C2×C3×C7×M16 | C2 | semidirect |
| 3. C7×#926 | C2 | semidirect |
| 4. C7×#821 | C2 | semidirect |
| 10. C2×C7×D12 | C4 | semidirect |
| 13. C2×C3×C7×C8 | C22 | semidirect |
| 15. C7×C4⋊Dic3 | C22 | semidirect |
| 18. C2×C7×M16 | D3 | semidirect |
| 21. #5131 | C7 | direct (N × H) |
| 42. C2×C7×C8 | C2×D3 | semidirect |
| 47. C2×C3×M16 | C2×C7 | semidirect |
| 48. #926 | C2×C7 | semidirect |
| 49. #821 | C2×C7 | semidirect |
| 78. C2×D12 | C4×C7 | semidirect |
| 81. C2×C3×C8 | C22×C7 | semidirect |
| 83. C4⋊Dic3 | C22×C7 | semidirect |
| 90. C2×M16 | D3×C7 | semidirect |
| 116. C3×C7 | #418 | semidirect |
| 124. C2×C8 | C2×D3×C7 | semidirect |
| 155. C7 | #5131 | direct (N × H) |
| 170. C3 | C7×#418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D12 | 2 |
| C2×C3×C7×M16 | 2 |
| C7×#926 | 2 |
| C7×#821 | 2 |
| C7×#418 | 3 |
| #5131 | 7 |