Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 3. #10620951 | C2 | semidirect |
| 5. C7×Dic3⋊C8 | C2 | semidirect |
| 6. C3×#6390 | C2 | semidirect |
| 7. #10620509 | C2 | semidirect |
| 28. #6390 | D3 | semidirect |
| 64. Dic3⋊C8 | D7 | semidirect |
| 76. C7×Dic3 | SD16 | semidirect |
| 145. C3×C7 | #461 | semidirect |
| 173. Dic3 | #1132 | semidirect |
| 190. C7 | #4818 | semidirect |
| 206. C3 | #89613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66623 | 2 |
| #10620990 | 2 |
| #10620951 | 2 |
| C2×#66566 | 2 |
| C7×Dic3⋊C8 | 2 |
| C3×#6390 | 2 |
| #10620509 | 2 |
| #89613 | 3 |
| #4818 | 7 |