Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
516 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 164 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 |
|---|---|---|
| 3. C2×Dic3×Dic7 | C2 | semidirect |
| 4. #10620670 | C2 | semidirect |
| 5. C3×C7⋊#95 | C2 | semidirect |
| 12. C2×C4×D3×C7 | C4 | semidirect |
| 14. (C2×D3)⋊Dic7 | C4 | semidirect |
| 20. C7⋊#95 | D3 | semidirect |
| 32. C2×Dic21 | C2×C4 | semidirect |
| 38. C2×C3×Dic7 | C2×C4 | semidirect |
| 62. C2×D3×C7 | C42 | semidirect |
| 66. C7×Dic3 | C22⋊C4 | semidirect |
| 84. C2×Dic7 | C4×D3 | semidirect |
| 91. C2×C4×D3 | Dic7 | semidirect |
| 136. C3×C7 | C4×C22⋊C4 | semidirect |
| 161. C2×D3 | C4×Dic7 | semidirect |
| 165. Dic3 | C22⋊Dic7 | semidirect |
| 183. C7 | #4666 | semidirect |
| 204. C3 | C4×C22⋊Dic7 | semidirect |
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×(C2×D3)⋊Dic7 | 2 |
| C2×Dic3×Dic7 | 2 |
| #10620670 | 2 |
| C3×C7⋊#95 | 2 |
| C4×C22⋊Dic7 | 3 |
| #4666 | 7 |