Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
212 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 69 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. #10621431 | C2 | semidirect |
| 3. #10621390 | C2 | semidirect |
| 4. C3×C7×#104 | C2 | semidirect |
| 5. #10620661 | C2 | semidirect |
| 6. #10620644 | C2 | semidirect |
| 7. C4×C3⋊(C7⋊C8) | C2 | semidirect |
| 13. #66635 | C4 | semidirect |
| 14. #66634 | C4 | semidirect |
| 15. #66633 | C4 | semidirect |
| 16. #66632 | C4 | semidirect |
| 27. C7×#104 | D3 | semidirect |
| 66. C3×#104 | D7 | semidirect |
| 119. #104 | D21 | semidirect |
| 145. C3×C7 | #443 | semidirect |
| 189. C7 | #4824 | semidirect |
| 202. C3 | #89596 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621433 | 2 |
| #10621431 | 2 |
| #10621390 | 2 |
| C3×C7×#104 | 2 |
| #10620661 | 2 |
| #10620644 | 2 |
| C4×C3⋊(C7⋊C8) | 2 |
| #89596 | 3 |
| #4824 | 7 |