Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
260 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 260 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 |
|---|---|---|
| 1. C2×D168 | C2 | semidirect |
| 2. C2×#66622 | C2 | semidirect |
| 3. #10621378 | C2 | semidirect |
| 4. C3×C7×#106 | C2 | semidirect |
| 5. #10620648 | C2 | semidirect |
| 19. C7×#106 | D3 | semidirect |
| 32. C3×C7×C8 | D4 | semidirect |
| 46. C3×#106 | D7 | semidirect |
| 69. C7×C8 | D12 | semidirect |
| 87. #106 | D21 | semidirect |
| 109. C3×C8 | D28 | semidirect |
| 111. C3×C7 | #469 | semidirect |
| 146. C8 | D84 | semidirect |
| 147. C7 | #4865 | semidirect |
| 162. C3 | #89637 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D168 | 2 |
| C2×#66622 | 2 |
| #10621378 | 2 |
| C3×C7×#106 | 2 |
| #10620648 | 2 |
| #89637 | 3 |
| #4865 | 7 |