Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
220 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 220 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 |
|---|---|---|
| 6. C4×Dic28 | C3 | direct (N × H) |
| 14. C3×Dic28 | C4 | direct (N × H) |
| 37. Dic28 | C3×C4 | direct (N × H) |
| 45. C3×C4×C7 | Q16 | semidirect |
| 78. C4×C7 | C3×Q16 | semidirect |
| 92. C3×C7 | C4×Q16 | semidirect |
| 108. C3×C4 | Dic28 | direct (N × H) |
| 120. C7 | C3×C4×Q16 | semidirect |
| 128. C4 | C3×Dic28 | direct (N × H) |
| 131. C3 | C4×Dic28 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic28 | 2 |
| C3×C4×Dic14 | 2 |
| C3×C4×C7×C8 | 2 |
| C3×#6392 | 2 |
| C3×#6390 | 2 |
| C4×Dic28 | 3 |
| C3×C4×Q16 | 7 |