Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
142 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 7. C22×Dic7 | C4 | semidirect |
| 9. C7×C22⋊C4 | C4 | semidirect |
| 13. C22⋊Dic7 | C4 | semidirect |
| 58. C22⋊C4 | Dic7 | semidirect |
| 81. C7 | #342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×C22⋊C4 | 2 |
| C2×C22⋊Dic7 | 2 |
| #342 | 7 |