Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
660 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 176 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. C7×C3⋊#95 | C2 | semidirect |
| 4. C3×C7⋊#95 | C2 | semidirect |
| 5. #10620529 | C2 | semidirect |
| 11. C2×C4×D21 | C4 | semidirect |
| 16. C2×D21⋊C4 | C4 | semidirect |
| 21. C7⋊#95 | D3 | semidirect |
| 30. C2×C3×C4×C7 | C2×C4 | semidirect |
| 32. C2×Dic21 | C2×C4 | semidirect |
| 36. C2×C7×Dic3 | C2×C4 | semidirect |
| 39. C2×C3×Dic7 | C2×C4 | semidirect |
| 55. C3⋊#95 | D7 | semidirect |
| 81. C2×C4×C7 | C4×D3 | semidirect |
| 86. C2×Dic7 | C4×D3 | semidirect |
| 104. D21 | #95 | semidirect |
| 134. C2×C3×C4 | C4×D7 | semidirect |
| 139. C2×Dic3 | C4×D7 | semidirect |
| 142. C3×C7 | C2×#95 | semidirect |
| 190. C2×C4 | D21⋊C4 | semidirect |
| 191. C7 | D3×#95 | semidirect |
| 212. C3 | D7×#95 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D21 | 2 |
| C22×D21⋊C4 | 2 |
| C7×C3⋊#95 | 2 |
| C3×C7⋊#95 | 2 |
| #10620529 | 2 |
| D7×#95 | 3 |
| D3×#95 | 7 |