Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
676 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 211 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×C7×#117 | C2 | semidirect |
| 3. #10621409 | C2 | semidirect |
| 4. #10621376 | C2 | semidirect |
| 5. C22⋊C4×D21 | C2 | semidirect |
| 6. C4×D84 | C2 | semidirect |
| 10. C2×D84 | C4 | semidirect |
| 13. C2×C4×D21 | C22 | semidirect |
| 14. C3×C7×C4⋊C4 | C22 | semidirect |
| 16. C3×C42×C7 | C22 | semidirect |
| 18. #66631 | C22 | semidirect |
| 19. C4⋊Dic21 | C22 | semidirect |
| 20. C4×Dic21 | C22 | semidirect |
| 22. C7×#117 | D3 | semidirect |
| 30. C22×D21 | C2×C4 | semidirect |
| 32. C2×C3×C4×C7 | C2×C4 | semidirect |
| 37. D84 | C2×C4 | semidirect |
| 38. D84 | C2×C4 | semidirect |
| 46. C7×C4⋊C4 | C2×D3 | semidirect |
| 48. C42×C7 | C2×D3 | semidirect |
| 54. C3×#117 | D7 | semidirect |
| 74. C2×C4×C7 | C4×D3 | semidirect |
| 88. C3×C4⋊C4 | C2×D7 | semidirect |
| 90. C3×C42 | C2×D7 | semidirect |
| 103. #117 | D21 | semidirect |
| 119. C2×C3×C4 | C4×D7 | semidirect |
| 127. C3×C7 | #518 | semidirect |
| 135. C4⋊C4 | C2×D21 | semidirect |
| 140. C42 | C2×D21 | semidirect |
| 163. C2×C4 | C4×D21 | semidirect |
| 167. C7 | #5521 | semidirect |
| 182. C3 | #90212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D84 | 2 |
| C3×C7×#117 | 2 |
| #10621409 | 2 |
| #10621376 | 2 |
| C22⋊C4×D21 | 2 |
| C4×D84 | 2 |
| #90212 | 3 |
| #5521 | 7 |