Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 80 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. #10620909 | C2 | semidirect |
| 3. C2×D21⋊C8 | C2 | semidirect |
| 4. C7×#835 | C2 | semidirect |
| 5. C3×#6409 | C2 | semidirect |
| 6. #10620504 | C2 | semidirect |
| 7. #10620503 | C2 | semidirect |
| 11. #66732 | C4 | semidirect |
| 27. #6409 | D3 | semidirect |
| 66. #835 | D7 | semidirect |
| 156. C3×C7 | #416 | semidirect |
| 206. C7 | #4804 | semidirect |
| 225. C3 | #89576 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66732 | 2 |
| #10620909 | 2 |
| C2×D21⋊C8 | 2 |
| C7×#835 | 2 |
| C3×#6409 | 2 |
| #10620504 | 2 |
| #10620503 | 2 |
| #89576 | 3 |
| #4804 | 7 |