Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 1. D4×Dic21 | C2 | semidirect |
| 3. #10620997 | C2 | semidirect |
| 4. C3×#6406 | C2 | semidirect |
| 5. #10620525 | C2 | semidirect |
| 6. #10620502 | C2 | semidirect |
| 7. #10620486 | C2 | semidirect |
| 16. C7×#213 | C4 | semidirect |
| 25. #6406 | D3 | semidirect |
| 32. C3×C7×D4 | C2×C4 | semidirect |
| 39. C7×D12 | C2×C4 | semidirect |
| 43. C7×C3⋊C8 | C2×C4 | semidirect |
| 74. Dic21 | D8 | semidirect |
| 82. C7×D4 | C4×D3 | semidirect |
| 99. #213 | Dic7 | semidirect |
| 132. C3×D4 | C2×Dic7 | semidirect |
| 140. D12 | C2×Dic7 | semidirect |
| 143. C3⋊C8 | C2×Dic7 | semidirect |
| 144. C3×C7 | C4×D8 | semidirect |
| 180. D4 | D3×Dic7 | semidirect |
| 190. C7 | #4756 | semidirect |
| 209. C3 | D8×Dic7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic21 | 2 |
| C2×C7×#213 | 2 |
| #10620997 | 2 |
| C3×#6406 | 2 |
| #10620525 | 2 |
| #10620502 | 2 |
| #10620486 | 2 |
| D8×Dic7 | 3 |
| #4756 | 7 |