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. C2×C3×C7×C22⋊C4 | C2 | semidirect |
| 3. C2×#66636 | C2 | semidirect |
| 4. C4×#4268 | C2 | semidirect |
| 5. #10621364 | C2 | semidirect |
| 6. C22⋊C4×D21 | C2 | semidirect |
| 7. #10621360 | C2 | semidirect |
| 11. C22×C3×C4×C7 | C22 | semidirect |
| 12. C2×#4268 | C4 | semidirect |
| 16. C22×Dic21 | C22 | semidirect |
| 17. C2×C4×D21 | C22 | semidirect |
| 19. C3×C7×C22⋊C4 | C22 | semidirect |
| 21. #66636 | C22 | semidirect |
| 22. #66631 | C22 | semidirect |
| 23. #66629 | C22 | semidirect |
| 24. C4×Dic21 | C22 | semidirect |
| 26. C2×C7×C22⋊C4 | D3 | semidirect |
| 34. C23×C3×C7 | C2×C4 | semidirect |
| 39. C22×D21 | C2×C4 | semidirect |
| 43. #4268 | C2×C4 | semidirect |
| 44. #4268 | C2×C4 | semidirect |
| 46. C2×Dic21 | C2×C4 | semidirect |
| 52. C22×C4×C7 | C2×D3 | semidirect |
| 60. C7×C22⋊C4 | C2×D3 | semidirect |
| 67. C2×C3×C22⋊C4 | D7 | semidirect |
| 89. C23×C7 | C4×D3 | semidirect |
| 107. C22×C3×C4 | C2×D7 | semidirect |
| 115. C3×C22⋊C4 | C2×D7 | semidirect |
| 133. C2×C22⋊C4 | D21 | semidirect |
| 149. C23×C3 | C4×D7 | semidirect |
| 165. C3×C7 | #518 | semidirect |
| 174. C22×C4 | C2×D21 | semidirect |
| 180. C22⋊C4 | C2×D21 | semidirect |
| 206. C23 | C4×D21 | semidirect |
| 219. C7 | #5486 | semidirect |
| 240. C3 | #90177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4268 | 2 |
| C2×C3×C7×C22⋊C4 | 2 |
| C2×#66636 | 2 |
| C4×#4268 | 2 |
| #10621364 | 2 |
| C22⋊C4×D21 | 2 |
| #10621360 | 2 |
| #90177 | 3 |
| #5486 | 7 |