Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 112 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×#66627 | C2 | semidirect |
| 3. C2×C3×C4⋊Dic7 | C2 | semidirect |
| 4. #10620507 | C2 | semidirect |
| 5. #10620501 | C2 | semidirect |
| 10. C7×#235 | C4 | semidirect |
| 20. C2×C4⋊Dic7 | D3 | semidirect |
| 34. C7×D12 | C2×C4 | semidirect |
| 37. C7×Dic6 | C2×C4 | semidirect |
| 91. #235 | Dic7 | semidirect |
| 132. D12 | C2×Dic7 | semidirect |
| 135. Dic6 | C2×Dic7 | semidirect |
| 137. C3×C7 | #417 | semidirect |
| 183. C7 | #4966 | semidirect |
| 201. C3 | #90004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#235 | 2 |
| C2×#66627 | 2 |
| C2×C3×C4⋊Dic7 | 2 |
| #10620507 | 2 |
| #10620501 | 2 |
| #90004 | 3 |
| #4966 | 7 |