Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
236 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 99 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. C3×C4×C7×C8 | C2 | semidirect |
| 4. #10620653 | C2 | semidirect |
| 5. C4×C3⋊(C7⋊C8) | C2 | semidirect |
| 17. C4×C7×C8 | D3 | semidirect |
| 31. C4×D21 | C8 | semidirect |
| 44. C3×C4×C8 | D7 | semidirect |
| 88. C4×C8 | D21 | semidirect |
| 111. C3×C7 | #431 | semidirect |
| 147. C7 | #4685 | semidirect |
| 162. C3 | #89457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×D21 | 2 |
| C3×C4×C7×C8 | 2 |
| #10620659 | 2 |
| #10620653 | 2 |
| C4×C3⋊(C7⋊C8) | 2 |
| #89457 | 3 |
| #4685 | 7 |