Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
208 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 64 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. #10620674 | C2 | semidirect |
| 4. C3×#6409 | C2 | semidirect |
| 5. #10620524 | C2 | semidirect |
| 6. #10620523 | C2 | semidirect |
| 23. #6409 | D3 | semidirect |
| 133. C3×C7 | #484 | semidirect |
| 174. C7 | #4811 | semidirect |
| 190. C3 | #89816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#946 | 2 |
| D3×C4⋊Dic7 | 2 |
| #10620674 | 2 |
| C3×#6409 | 2 |
| #10620524 | 2 |
| #10620523 | 2 |
| (C2×D3)⋊(C7⋊C8) | 2 |
| #89816 | 3 |
| #4811 | 7 |