Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 80 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. C7×D4×Dic3 | C2 | semidirect |
| 3. #10620990 | C2 | semidirect |
| 4. C3×#6406 | C2 | semidirect |
| 5. #10620524 | C2 | semidirect |
| 6. #10620504 | C2 | semidirect |
| 7. Dic3×C7⋊C8 | C2 | semidirect |
| 13. #66632 | C4 | semidirect |
| 24. #6406 | D3 | semidirect |
| 32. C3×C7×D4 | C2×C4 | semidirect |
| 35. D84 | C2×C4 | semidirect |
| 42. C3⋊(C7⋊C8) | C2×C4 | semidirect |
| 56. D4×Dic3 | D7 | semidirect |
| 75. C7×Dic3 | D8 | semidirect |
| 80. C7×D4 | C4×D3 | semidirect |
| 132. C3×D4 | C4×D7 | semidirect |
| 144. C3×C7 | C4×D8 | semidirect |
| 174. Dic3 | #1141 | semidirect |
| 180. D4 | D21⋊C4 | semidirect |
| 190. C7 | #4756 | semidirect |
| 209. C3 | C4×#1141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66632 | 2 |
| C7×D4×Dic3 | 2 |
| #10620990 | 2 |
| C3×#6406 | 2 |
| #10620524 | 2 |
| #10620504 | 2 |
| Dic3×C7⋊C8 | 2 |
| C4×#1141 | 3 |
| #4756 | 7 |