Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
304 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 78 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. C3×C7×#124 | C2 | semidirect |
| 3. C7×#942 | C2 | semidirect |
| 4. C7×#833 | C2 | semidirect |
| 5. C7×#805 | C2 | semidirect |
| 7. C2×C3×C7×Q8 | C22 | semidirect |
| 14. C3×C42×C7 | C22 | semidirect |
| 17. C7×#208 | C22 | semidirect |
| 20. C7×#124 | D3 | semidirect |
| 23. #5061 | C7 | direct (N × H) |
| 40. C2×C7×Q8 | C2×D3 | semidirect |
| 48. C42×C7 | C2×D3 | semidirect |
| 50. C3×#124 | C2×C7 | semidirect |
| 51. #942 | C2×C7 | semidirect |
| 52. #833 | C2×C7 | semidirect |
| 53. #805 | C2×C7 | semidirect |
| 78. C2×C3×Q8 | C22×C7 | semidirect |
| 85. C3×C42 | C22×C7 | semidirect |
| 88. #208 | C22×C7 | semidirect |
| 95. #124 | D3×C7 | semidirect |
| 121. C3×C7 | #455 | semidirect |
| 124. C2×Q8 | C2×D3×C7 | semidirect |
| 132. C42 | C2×D3×C7 | semidirect |
| 160. C7 | #5061 | direct (N × H) |
| 174. C3 | C7×#455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1004 | 2 |
| C3×C7×#124 | 2 |
| C7×#942 | 2 |
| C7×#833 | 2 |
| C7×#805 | 2 |
| C7×#455 | 3 |
| #5061 | 7 |