Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
192 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 60 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. #10620646 | C2 | semidirect |
| 4. C3×#6384 | C2 | semidirect |
| 5. #10620520 | C2 | semidirect |
| 6. #10620505 | C2 | semidirect |
| 24. #6384 | D3 | semidirect |
| 130. C3×C7 | #485 | semidirect |
| 170. C7 | #4815 | semidirect |
| 186. C3 | #89768 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#892 | 2 |
| #10620931 | 2 |
| #10620646 | 2 |
| C3×#6384 | 2 |
| #10620520 | 2 |
| #10620505 | 2 |
| (C2×D3)⋊(C7⋊C8) | 2 |
| #89768 | 3 |
| #4815 | 7 |