Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
330 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 167 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×C7×C4⋊C4 | C2 | semidirect |
| 4. C2×C4⋊Dic7 | C2 | semidirect |
| 5. C2×C4×Dic7 | C2 | semidirect |
| 6. #6455 | C2 | direct (N × H) |
| 12. C2×C4×D7 | C4 | semidirect |
| 14. C7×C4⋊C4 | C22 | semidirect |
| 16. C4⋊Dic7 | C22 | semidirect |
| 17. C4×Dic7 | C22 | semidirect |
| 32. C4×D7 | C2×C4 | semidirect |
| 36. C2×C4⋊C4 | D7 | semidirect |
| 59. C4⋊C4 | C2×D7 | semidirect |
| 62. C2×C7 | #117 | semidirect |
| 81. C7 | C2×#117 | semidirect |
| 95. C2 | #6455 | 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×C7×C4⋊C4 | 2 |
| C2×(C2×D7)⋊C4 | 2 |
| C2×C4⋊Dic7 | 2 |
| C2×C4×Dic7 | 2 |
| #6455 | 2 |
| C2×#117 | 7 |