Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 68 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. #10620938 | C2 | semidirect |
| 5. #10620655 | C2 | semidirect |
| 6. C3×Dic7⋊C8 | C2 | semidirect |
| 7. #10620508 | C2 | semidirect |
| 28. Dic7⋊C8 | D3 | semidirect |
| 75. C3×Dic7 | SD16 | semidirect |
| 128. Dic7 | #204 | semidirect |
| 145. C3×C7 | #461 | semidirect |
| 190. C7 | #4841 | semidirect |
| 206. C3 | #89934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#204 | 2 |
| D12×Dic7 | 2 |
| #10620938 | 2 |
| C2×#66567 | 2 |
| #10620655 | 2 |
| C3×Dic7⋊C8 | 2 |
| #10620508 | 2 |
| #89934 | 3 |
| #4841 | 7 |