Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×C42×C7 | C2 | semidirect |
| 4. C2×C4×Dic7 | C2 | semidirect |
| 5. C7⋊#95 | C2 | semidirect |
| 13. C2×C4×D7 | C4 | semidirect |
| 15. (C2×D7)⋊C4 | C4 | direct (N × H) |
| 27. C2×C4×C7 | C2×C4 | semidirect |
| 35. C2×Dic7 | C2×C4 | semidirect |
| 40. C2×C42 | D7 | semidirect |
| 51. C2×D7 | C42 | semidirect |
| 53. C4×C7 | C22⋊C4 | semidirect |
| 89. C2×C4 | C4×D7 | semidirect |
| 92. C7 | C4×C22⋊C4 | semidirect |
| 106. C4 | (C2×D7)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D7 | 2 |
| C2×C42×C7 | 2 |
| C2×(C2×D7)⋊C4 | 2 |
| C2×C4×Dic7 | 2 |
| C7⋊#95 | 2 |
| C4×C22⋊C4 | 7 |