Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
244 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 88 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. Dic6×Dic7 | C2 | semidirect |
| 4. #10620656 | C2 | semidirect |
| 5. C3×C8×Dic7 | C2 | semidirect |
| 6. #10620508 | C2 | semidirect |
| 15. C7×#204 | C4 | semidirect |
| 27. C8×Dic7 | D3 | semidirect |
| 37. C7×Dic6 | C2×C4 | semidirect |
| 41. C3×C7×C8 | C2×C4 | semidirect |
| 71. C3×Dic7 | SD16 | semidirect |
| 86. C7×C8 | C4×D3 | semidirect |
| 99. #204 | Dic7 | direct (N × H) |
| 121. Dic7 | #204 | direct (N × H) |
| 133. Dic6 | C2×Dic7 | semidirect |
| 135. C3×C8 | C2×Dic7 | semidirect |
| 136. C3×C7 | C4×SD16 | semidirect |
| 177. C8 | D3×Dic7 | semidirect |
| 178. C7 | C4×#204 | semidirect |
| 194. C3 | SD16×Dic7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#204 | 2 |
| D12×Dic7 | 2 |
| Dic6×Dic7 | 2 |
| #10620656 | 2 |
| C3×C8×Dic7 | 2 |
| #10620508 | 2 |
| #10620502 | 2 |
| SD16×Dic7 | 3 |
| C4×#204 | 7 |