Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
660 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 243 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×C4⋊C4 | C2 | semidirect |
| 4. C2×C4⋊Dic21 | C2 | semidirect |
| 5. C2×C4×Dic21 | C2 | semidirect |
| 6. #10621375 | C2 | direct (N × H) |
| 13. C2×C4×D21 | C4 | semidirect |
| 15. C3×C7×C4⋊C4 | C22 | semidirect |
| 17. C4⋊Dic21 | C22 | semidirect |
| 18. C4×Dic21 | C22 | semidirect |
| 20. C2×C7×C4⋊C4 | D3 | semidirect |
| 39. C4×D21 | C2×C4 | semidirect |
| 47. C7×C4⋊C4 | C2×D3 | semidirect |
| 52. C2×C3×C4⋊C4 | D7 | semidirect |
| 91. C3×C4⋊C4 | C2×D7 | semidirect |
| 95. C2×C3×C7 | #117 | semidirect |
| 103. C2×C4⋊C4 | D21 | semidirect |
| 132. C3×C7 | C2×#117 | semidirect |
| 141. C4⋊C4 | C2×D21 | semidirect |
| 144. C2×C7 | #892 | semidirect |
| 175. C7 | C2×#892 | semidirect |
| 176. C2×C3 | #6455 | semidirect |
| 193. C3 | C2×#6455 | semidirect |
| 195. C2 | #10621375 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D21 | 2 |
| C2×C3×C7×C4⋊C4 | 2 |
| C2×#66631 | 2 |
| C2×C4⋊Dic21 | 2 |
| C2×C4×Dic21 | 2 |
| #10621375 | 2 |
| C2×#6455 | 3 |
| C2×#892 | 7 |