Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
392 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 182 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×#6507 | C2 | semidirect |
| 4. C3×#6442 | C2 | semidirect |
| 5. C3×#6441 | C2 | semidirect |
| 6. C3×#6433 | C2 | semidirect |
| 7. #90363 | C3 | direct (N × H) |
| 23. #6507 | C2×C3 | semidirect |
| 25. #6442 | C2×C3 | semidirect |
| 26. #6441 | C2×C3 | semidirect |
| 27. #6433 | C2×C3 | semidirect |
| 119. C3×C7 | #563 | semidirect |
| 155. C7 | C3×#563 | semidirect |
| 167. C3 | #90363 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#124 | 2 |
| C3×#6507 | 2 |
| C3×#6498 | 2 |
| C3×#6442 | 2 |
| C3×#6441 | 2 |
| C3×#6433 | 2 |
| #90363 | 3 |
| C3×#563 | 7 |