Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 64 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. #10621378 | C2 | semidirect |
| 2. #10621027 | C2 | semidirect |
| 3. C2×#66561 | C2 | semidirect |
| 4. C2×D21⋊C8 | C2 | semidirect |
| 5. C7×#807 | C2 | semidirect |
| 6. C3×#6383 | C2 | semidirect |
| 7. #10620504 | C2 | semidirect |
| 28. #6383 | D3 | semidirect |
| 46. C7×C3⋊C8 | D4 | semidirect |
| 66. #807 | D7 | semidirect |
| 73. C2×D21 | D8 | semidirect |
| 157. C3⋊C8 | D28 | semidirect |
| 158. C3×C7 | #466 | semidirect |
| 210. C7 | #4775 | semidirect |
| 232. C3 | #89655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621378 | 2 |
| #10621027 | 2 |
| C2×#66561 | 2 |
| C2×D21⋊C8 | 2 |
| C7×#807 | 2 |
| C3×#6383 | 2 |
| #10620504 | 2 |
| #89655 | 3 |
| #4775 | 7 |