Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
572 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 144 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. C23×C3×Dic7 | C2 | semidirect |
| 3. C2×C7×#217 | C2 | semidirect |
| 4. C2×#66575 | C2 | semidirect |
| 5. #10620529 | C2 | semidirect |
| 11. C2×#4268 | C4 | semidirect |
| 20. C23×Dic7 | D3 | semidirect |
| 35. C22×D21 | C2×C4 | semidirect |
| 39. C2×Dic21 | C2×C4 | semidirect |
| 46. C2×C3×Dic7 | D4 | semidirect |
| 61. C2×#217 | D7 | semidirect |
| 68. C22×C3×C7 | C22⋊C4 | semidirect |
| 104. C2×Dic7 | #67 | semidirect |
| 133. C22×C7 | (C2×D3)⋊C4 | semidirect |
| 169. C3×C7 | #386 | semidirect |
| 193. C22×C3 | (C2×D7)⋊C4 | semidirect |
| 229. C7 | #5213 | semidirect |
| 246. C22 | #66575 | semidirect |
| 255. C3 | #89730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4268 | 2 |
| C23×C3×Dic7 | 2 |
| C2×C7×#217 | 2 |
| C2×#66575 | 2 |
| #10620529 | 2 |
| #89730 | 3 |
| #5213 | 7 |