Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 82 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. C7×#938 | C2 | semidirect |
| 2. C2×C7×#213 | C2 | semidirect |
| 3. C2×D3×C7×C8 | C2 | semidirect |
| 4. C7×#895 | C2 | semidirect |
| 5. C3×C7×#102 | C2 | semidirect |
| 6. C7×#821 | C2 | semidirect |
| 7. C7×#807 | C2 | semidirect |
| 28. C7×#102 | D3 | semidirect |
| 29. #4775 | C7 | direct (N × H) |
| 46. C7×C3⋊C8 | D4 | semidirect |
| 60. #938 | C2×C7 | semidirect |
| 61. C2×#213 | C2×C7 | semidirect |
| 62. C2×D3×C8 | C2×C7 | semidirect |
| 63. #895 | C2×C7 | semidirect |
| 64. C3×#102 | C2×C7 | semidirect |
| 65. #821 | C2×C7 | semidirect |
| 66. #807 | C2×C7 | semidirect |
| 76. C2×D3×C7 | D8 | semidirect |
| 125. #102 | D3×C7 | semidirect |
| 157. C3⋊C8 | C7×D4 | semidirect |
| 158. C3×C7 | #466 | semidirect |
| 187. C2×D3 | C7×D8 | semidirect |
| 210. C7 | #4775 | direct (N × H) |
| 232. C3 | C7×#466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#938 | 2 |
| C2×C7×#213 | 2 |
| C2×D3×C7×C8 | 2 |
| C7×#895 | 2 |
| C3×C7×#102 | 2 |
| C7×#821 | 2 |
| C7×#807 | 2 |
| C7×#466 | 3 |
| #4775 | 7 |