Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 268 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×#121 | C2 | semidirect |
| 2. C2×C7×#213 | C2 | semidirect |
| 3. C7×#930 | C2 | semidirect |
| 4. C22×C7×C3⋊C8 | C2 | semidirect |
| 5. C7×#832 | C2 | semidirect |
| 6. C7×#809 | C2 | semidirect |
| 7. C7×#807 | C2 | semidirect |
| 25. C7×#121 | D3 | semidirect |
| 29. #5038 | C7 | direct (N × H) |
| 46. C7×C3⋊C8 | D4 | semidirect |
| 60. C3×#121 | C2×C7 | semidirect |
| 61. C2×#213 | C2×C7 | semidirect |
| 62. #930 | C2×C7 | semidirect |
| 63. C22×C3⋊C8 | C2×C7 | semidirect |
| 64. #832 | C2×C7 | semidirect |
| 65. #809 | C2×C7 | semidirect |
| 66. #807 | C2×C7 | semidirect |
| 72. C22×C3×C7 | D8 | semidirect |
| 122. #121 | D3×C7 | semidirect |
| 134. C22×C7 | #213 | semidirect |
| 157. C3⋊C8 | C7×D4 | semidirect |
| 158. C3×C7 | #466 | semidirect |
| 183. C22×C3 | C7×D8 | semidirect |
| 210. C7 | #5038 | direct (N × H) |
| 225. C22 | C7×#213 | semidirect |
| 232. C3 | C7×#466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#121 | 2 |
| C2×C7×#213 | 2 |
| C7×#930 | 2 |
| C22×C7×C3⋊C8 | 2 |
| C7×#832 | 2 |
| C7×#809 | 2 |
| C7×#807 | 2 |
| C7×#466 | 3 |
| #5038 | 7 |