Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 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. C7⋊#95 | C2 | semidirect |
| 9. C22×Dic7 | C4 | semidirect |
| 13. C7×C22⋊C4 | C4 | semidirect |
| 14. C22⋊Dic7 | C4 | semidirect |
| 25. C2×C4×C7 | C2×C4 | semidirect |
| 32. C2×Dic7 | C2×C4 | semidirect |
| 43. C22×C7 | C42 | semidirect |
| 52. Dic7 | C22⋊C4 | direct (N × H) |
| 61. C22⋊C4 | Dic7 | direct (N × H) |
| 85. C2×C4 | C2×Dic7 | semidirect |
| 86. C7 | C4×C22⋊C4 | semidirect |
| 91. C22 | C4×Dic7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic7 | 2 |
| C2×C7×C22⋊C4 | 2 |
| C2×C22⋊Dic7 | 2 |
| C2×C4×Dic7 | 2 |
| C7⋊#95 | 2 |
| C4×C22⋊C4 | 7 |