Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
468 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 468 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 |
|---|---|---|
| 4. C2×#66577 | C2 | semidirect |
| 5. #10620529 | C2 | semidirect |
| 14. #66636 | C4 | semidirect |
| 31. C2×Dic21 | C2×C4 | semidirect |
| 59. C22×C3×C7 | C4⋊C4 | semidirect |
| 112. C22×C7 | Dic3⋊C4 | semidirect |
| 139. C3×C7 | #385 | semidirect |
| 160. C22×C3 | Dic7⋊C4 | semidirect |
| 187. C7 | #5210 | semidirect |
| 198. C22 | #66577 | semidirect |
| 208. C3 | #89718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×Dic7 | 2 |
| C2×#66636 | 2 |
| C2×C7×#217 | 2 |
| C2×#66577 | 2 |
| #10620529 | 2 |
| #89718 | 3 |
| #5210 | 7 |