Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
200 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 74 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. C3×#6451 | C2 | semidirect |
| 5. C3×#6390 | C2 | semidirect |
| 6. C3×#6389 | C2 | semidirect |
| 7. C3×#6384 | C2 | semidirect |
| 8. #89537 | C3 | direct (N × H) |
| 21. #6451 | C2×C3 | semidirect |
| 24. #6390 | C2×C3 | semidirect |
| 25. #6389 | C2×C3 | semidirect |
| 26. #6384 | C2×C3 | semidirect |
| 133. C3×C7 | #489 | semidirect |
| 174. C7 | C3×#489 | semidirect |
| 190. C3 | #89537 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6499 | 2 |
| C3×#6451 | 2 |
| C3×C7×#102 | 2 |
| C3×#6406 | 2 |
| C3×#6390 | 2 |
| C3×#6389 | 2 |
| C3×#6384 | 2 |
| #89537 | 3 |
| C3×#489 | 7 |