Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
204 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 69 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. #10621353 | C2 | semidirect |
| 3. C3×C7×C4⋊C8 | C2 | semidirect |
| 6. #10620657 | C2 | semidirect |
| 7. #10620656 | C2 | semidirect |
| 22. C7×C4⋊C8 | D3 | semidirect |
| 53. C3×C4⋊C8 | D7 | semidirect |
| 101. C4⋊C8 | D21 | semidirect |
| 127. C3×C7 | #478 | semidirect |
| 166. C7 | #4847 | semidirect |
| 182. C3 | #89619 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D84 | 2 |
| #10621353 | 2 |
| C3×C7×C4⋊C8 | 2 |
| #10620660 | 2 |
| #10620657 | 2 |
| #10620656 | 2 |
| #89619 | 3 |
| #4847 | 7 |