Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
180 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 92 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. #10620651 | C2 | semidirect |
| 3. C3×#6386 | C2 | semidirect |
| 4. #10620470 | C2 | semidirect |
| 5. D3×C7⋊C16 | C2 | semidirect |
| 14. C3⋊(C7⋊C16) | C22 | semidirect |
| 15. C3×C7⋊C16 | C22 | semidirect |
| 19. #6386 | D3 | direct (N × H) |
| 41. C7⋊C16 | C2×D3 | semidirect |
| 79. D3×C7 | M32 | semidirect |
| 104. C3×C7 | C2×M32 | semidirect |
| 137. C7 | D3×M32 | semidirect |
| 141. D3 | #6386 | direct (N × H) |
| 150. C3 | C2×#6386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C7×C8 | 2 |
| #10620651 | 2 |
| C3×#6386 | 2 |
| #10620470 | 2 |
| D3×C7⋊C16 | 2 |
| C2×#6386 | 3 |
| D3×M32 | 7 |