Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
300 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 110 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. C3×C7×#103 | C2 | semidirect |
| 5. C3×#6409 | C2 | semidirect |
| 6. C3×#6390 | C2 | semidirect |
| 7. C3×#6384 | C2 | semidirect |
| 8. #89574 | C3 | direct (N × H) |
| 11. C3×Q8×D7 | C4 | semidirect |
| 26. C7×#103 | C2×C3 | semidirect |
| 27. #6409 | C2×C3 | semidirect |
| 28. #6390 | C2×C3 | semidirect |
| 29. #6384 | C2×C3 | semidirect |
| 50. Q8×D7 | C3×C4 | semidirect |
| 68. C3×#103 | D7 | semidirect |
| 122. #103 | C3×D7 | semidirect |
| 151. C3×C7 | #419 | semidirect |
| 198. C7 | C3×#419 | semidirect |
| 214. C3 | #89574 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q8×D7 | 2 |
| C2×C3×#1131 | 2 |
| C3×#6455 | 2 |
| C3×C7×#103 | 2 |
| C3×#6409 | 2 |
| C3×#6390 | 2 |
| C3×#6384 | 2 |
| #89574 | 3 |
| C3×#419 | 7 |