Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
476 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 102 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×#66631 | C2 | semidirect |
| 3. C2×C7×(C2×D3)⋊C4 | C2 | semidirect |
| 4. C2×C3×Dic7⋊C4 | C2 | semidirect |
| 5. C2×#66575 | C2 | semidirect |
| 6. C2×(C2×D3)⋊Dic7 | C2 | semidirect |
| 7. #10620529 | C2 | semidirect |
| 29. C2×Dic7⋊C4 | D3 | semidirect |
| 61. C2×C3×Dic7 | D4 | semidirect |
| 83. C2×(C2×D3)⋊C4 | D7 | semidirect |
| 141. C2×Dic7 | D12 | semidirect |
| 231. C3×C7 | #394 | semidirect |
| 313. C7 | #4991 | semidirect |
| 349. C3 | #89731 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4247 | 2 |
| C2×#66631 | 2 |
| C2×C7×(C2×D3)⋊C4 | 2 |
| C2×C3×Dic7⋊C4 | 2 |
| C2×#66575 | 2 |
| C2×(C2×D3)⋊Dic7 | 2 |
| #10620529 | 2 |
| #89731 | 3 |
| #4991 | 7 |