Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
190 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 75 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×C4⋊Dic7 | C2 | semidirect |
| 5. C2×C4×Dic7 | C2 | semidirect |
| 6. C7⋊#95 | C2 | semidirect |
| 7. C7⋊#95 | C2 | semidirect |
| 15. C7×C22⋊C4 | C4 | semidirect |
| 84. C22⋊C4 | Dic7 | semidirect |
| 120. C7 | #388 | 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 |
| C2×C4⋊Dic7 | 2 |
| C2×C4×Dic7 | 2 |
| C7⋊#95 | 2 |
| #388 | 7 |