Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
660 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 272 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×C4⋊Dic21 | C2 | semidirect |
| 3. C2×C3×C4⋊Dic7 | C2 | semidirect |
| 5. C2×Dic3×Dic7 | C2 | semidirect |
| 6. #10620900 | C2 | direct (N × H) |
| 12. C2×C4×D3×C7 | C4 | semidirect |
| 15. C4⋊Dic21 | C22 | semidirect |
| 16. C3×C4⋊Dic7 | C22 | semidirect |
| 18. Dic3×Dic7 | C22 | semidirect |
| 23. C2×C4⋊Dic7 | D3 | semidirect |
| 37. C4×D3×C7 | C2×C4 | semidirect |
| 49. C4⋊Dic7 | C2×D3 | semidirect |
| 89. C2×C4×D3 | Dic7 | semidirect |
| 95. C2×C3×C7 | #117 | semidirect |
| 131. C4×D3 | C2×Dic7 | semidirect |
| 132. C3×C7 | C2×#117 | semidirect |
| 145. C2×C7 | #892 | semidirect |
| 175. C7 | C2×#892 | semidirect |
| 176. C2×C3 | #6489 | semidirect |
| 193. C3 | C2×#6489 | semidirect |
| 195. C2 | #10620900 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D3×C7 | 2 |
| C2×C4⋊Dic21 | 2 |
| C2×C3×C4⋊Dic7 | 2 |
| C2×(C2×D3)⋊Dic7 | 2 |
| C2×Dic3×Dic7 | 2 |
| #10620900 | 2 |
| C2×#6489 | 3 |
| C2×#892 | 7 |