Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
300 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 300 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 |
|---|---|---|
| 4. C7×#835 | C2 | semidirect |
| 5. C3×#6409 | C2 | semidirect |
| 6. #10620510 | C2 | semidirect |
| 7. #10620509 | C2 | semidirect |
| 11. Q8×D21 | C4 | semidirect |
| 27. #6409 | D3 | semidirect |
| 66. #835 | D7 | semidirect |
| 151. C3×C7 | #419 | semidirect |
| 198. C7 | #4802 | semidirect |
| 214. C3 | #89574 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D21 | 2 |
| #10620909 | 2 |
| C2×#66559 | 2 |
| C7×#835 | 2 |
| C3×#6409 | 2 |
| #10620510 | 2 |
| #10620509 | 2 |
| #89574 | 3 |
| #4802 | 7 |