Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
320 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 320 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×#123 | C2 | semidirect |
| 3. C7×#929 | C2 | semidirect |
| 4. C7×#834 | C2 | semidirect |
| 5. C7×#806 | C2 | semidirect |
| 8. C22×C3×C4×C7 | C22 | semidirect |
| 16. C3×C7×C22⋊C4 | C22 | semidirect |
| 17. C7×#217 | C22 | semidirect |
| 22. C7×#123 | D3 | semidirect |
| 25. #5053 | C7 | direct (N × H) |
| 50. C22×C4×C7 | C2×D3 | semidirect |
| 56. C7×C22⋊C4 | C2×D3 | semidirect |
| 58. C3×#123 | C2×C7 | semidirect |
| 59. #929 | C2×C7 | semidirect |
| 60. #834 | C2×C7 | semidirect |
| 61. #806 | C2×C7 | semidirect |
| 95. C22×C3×C4 | C22×C7 | semidirect |
| 103. C3×C22⋊C4 | C22×C7 | semidirect |
| 104. #217 | C22×C7 | semidirect |
| 114. #123 | D3×C7 | semidirect |
| 148. C3×C7 | #458 | semidirect |
| 155. C22×C4 | C2×D3×C7 | semidirect |
| 161. C22⋊C4 | C2×D3×C7 | semidirect |
| 198. C7 | #5053 | direct (N × H) |
| 217. C3 | C7×#458 | 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×#123 | 2 |
| C7×#929 | 2 |
| C7×#834 | 2 |
| C7×#806 | 2 |
| C7×#458 | 3 |
| #5053 | 7 |