Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
192 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 78 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×#6392 | C2 | semidirect |
| 5. C3×#6391 | C2 | semidirect |
| 6. C3×#6390 | C2 | semidirect |
| 7. C3×#6390 | C2 | semidirect |
| 8. #89495 | C3 | direct (N × H) |
| 23. #6392 | C2×C3 | semidirect |
| 24. #6391 | C2×C3 | semidirect |
| 25. #6390 | C2×C3 | semidirect |
| 26. #6390 | C2×C3 | semidirect |
| 130. C3×C7 | #485 | semidirect |
| 170. C7 | C3×#485 | semidirect |
| 186. C3 | #89495 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6489 | 2 |
| C3×#6487 | 2 |
| C3×C7×C22⋊C8 | 2 |
| C3×#6392 | 2 |
| C3×#6391 | 2 |
| C3×#6390 | 2 |
| #89495 | 3 |
| C3×#485 | 7 |