Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
572 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 148 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. C23×Dic21 | C2 | semidirect |
| 3. C2×C3×C22⋊Dic7 | C2 | semidirect |
| 4. C2×(C2×D3)⋊Dic7 | C2 | semidirect |
| 5. #10620529 | C2 | semidirect |
| 14. C2×C7×#67 | C4 | semidirect |
| 22. C2×C22⋊Dic7 | D3 | semidirect |
| 35. C22×D3×C7 | C2×C4 | semidirect |
| 39. C2×Dic21 | D4 | semidirect |
| 43. C2×C7×Dic3 | C2×C4 | semidirect |
| 68. C22×C3×C7 | C22⋊C4 | semidirect |
| 110. C2×#67 | Dic7 | semidirect |
| 138. C22×C7 | (C2×D3)⋊C4 | semidirect |
| 157. C22×D3 | C2×Dic7 | semidirect |
| 168. C2×Dic3 | C2×Dic7 | semidirect |
| 169. C3×C7 | #386 | semidirect |
| 193. C22×C3 | C22⋊Dic7 | semidirect |
| 229. C7 | #4958 | semidirect |
| 246. C22 | (C2×D3)⋊Dic7 | semidirect |
| 255. C3 | #89992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic21 | 2 |
| C22×C7×#67 | 2 |
| C2×C3×C22⋊Dic7 | 2 |
| C2×(C2×D3)⋊Dic7 | 2 |
| #10620529 | 2 |
| #89992 | 3 |
| #4958 | 7 |