Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
212 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 60 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×#892 | C2 | semidirect |
| 3. #10620648 | C2 | semidirect |
| 4. C3×#6381 | C2 | semidirect |
| 5. #10620521 | C2 | semidirect |
| 6. #10620504 | C2 | semidirect |
| 7. (C2×D3)⋊(C7⋊C8) | C2 | semidirect |
| 26. #6381 | D3 | semidirect |
| 54. #892 | D7 | semidirect |
| 138. C3×C7 | #482 | semidirect |
| 182. C7 | #4885 | semidirect |
| 201. C3 | #89775 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#892 | 2 |
| #10621022 | 2 |
| #10620648 | 2 |
| C3×#6381 | 2 |
| #10620521 | 2 |
| #10620504 | 2 |
| (C2×D3)⋊(C7⋊C8) | 2 |
| #89775 | 3 |
| #4885 | 7 |