Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
304 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×C3×#1142 | C2 | semidirect |
| 3. C2×C3×Dic28 | C2 | semidirect |
| 4. C3×#6460 | C2 | semidirect |
| 5. C3×C7×#102 | C2 | semidirect |
| 6. C3×(C2×D7)⋊C8 | C2 | semidirect |
| 7. C3×#6384 | C2 | semidirect |
| 8. #89555 | C3 | direct (N × H) |
| 25. C2×#1142 | C2×C3 | semidirect |
| 26. C2×Dic28 | C2×C3 | semidirect |
| 27. #6460 | C2×C3 | semidirect |
| 28. C7×#102 | C2×C3 | semidirect |
| 29. (C2×D7)⋊C8 | C2×C3 | semidirect |
| 30. #6384 | C2×C3 | semidirect |
| 71. C3×#102 | D7 | semidirect |
| 131. #102 | C3×D7 | semidirect |
| 165. C3×C7 | #452 | semidirect |
| 218. C7 | C3×#452 | semidirect |
| 237. C3 | #89555 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1159 | 2 |
| C2×C3×#1142 | 2 |
| C2×C3×Dic28 | 2 |
| C3×#6460 | 2 |
| C3×C7×#102 | 2 |
| C3×(C2×D7)⋊C8 | 2 |
| C3×#6384 | 2 |
| #89555 | 3 |
| C3×#452 | 7 |