Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
228 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 3. C2×C3×Dic28 | C2 | semidirect |
| 4. C3×#6392 | C2 | semidirect |
| 5. C3×#6390 | C2 | semidirect |
| 6. #89888 | C3 | direct (N × H) |
| 18. C2×Dic28 | C2×C3 | semidirect |
| 19. #6392 | C2×C3 | semidirect |
| 20. #6390 | C2×C3 | semidirect |
| 49. C22×C3×C7 | Q16 | semidirect |
| 88. C22×C7 | C3×Q16 | semidirect |
| 106. C3×C7 | #467 | semidirect |
| 122. C22×C3 | Dic28 | semidirect |
| 140. C7 | C3×#467 | semidirect |
| 147. C22 | C3×Dic28 | semidirect |
| 154. C3 | #89888 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C7×C8 | 2 |
| C3×#6487 | 2 |
| C2×C3×Dic28 | 2 |
| C3×#6392 | 2 |
| C3×#6390 | 2 |
| #89888 | 3 |
| C3×#467 | 7 |