Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
280 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 1. C3×C7×#127 | C2 | semidirect |
| 2. C2×C3×#1141 | C2 | semidirect |
| 3. C3×C4×D28 | C2 | semidirect |
| 4. C3×#6406 | C2 | semidirect |
| 5. C3×C4⋊(C7⋊C8) | C2 | semidirect |
| 6. #89844 | C3 | direct (N × H) |
| 17. C7×#127 | C2×C3 | semidirect |
| 18. C2×#1141 | C2×C3 | semidirect |
| 19. C4×D28 | C2×C3 | semidirect |
| 20. #6406 | C2×C3 | semidirect |
| 21. C4⋊(C7⋊C8) | C2×C3 | semidirect |
| 34. C3×D28 | D4 | semidirect |
| 48. C3×#127 | D7 | semidirect |
| 60. C3×C4×C7 | D8 | semidirect |
| 76. D28 | C3×D4 | semidirect |
| 95. #127 | C3×D7 | semidirect |
| 107. C4×C7 | C3×D8 | semidirect |
| 125. C3×C7 | #459 | semidirect |
| 150. C3×C4 | #1141 | semidirect |
| 167. C7 | C3×#459 | semidirect |
| 182. C4 | C3×#1141 | semidirect |
| 185. C3 | #89844 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#127 | 2 |
| C2×C3×#1141 | 2 |
| C3×C4×D28 | 2 |
| C3×#6406 | 2 |
| C3×C4⋊(C7⋊C8) | 2 |
| #89844 | 3 |
| C3×#459 | 7 |