Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
674 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 674 conjugacy classes of subgroups — too many to draw. Only its 207 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. C22×C4×D7 | C2 | semidirect |
| 3. C2×C7×C22⋊C4 | C2 | semidirect |
| 4. C2×C22⋊Dic7 | C2 | semidirect |
| 5. C2×(C2×D7)⋊C4 | C2 | semidirect |
| 6. D7×C22⋊C4 | C2 | direct (N × H) |
| 9. C23×D7 | C4 | semidirect |
| 13. C22×C4×C7 | C22 | semidirect |
| 14. C22×Dic7 | C22 | semidirect |
| 16. C2×C4×D7 | C22 | semidirect |
| 17. C7×C22⋊C4 | C22 | semidirect |
| 18. C22⋊Dic7 | C22 | semidirect |
| 19. (C2×D7)⋊C4 | C22 | semidirect |
| 22. C23×C7 | C2×C4 | semidirect |
| 29. C22×D7 | C2×C4 | semidirect |
| 30. C22×D7 | C2×C4 | semidirect |
| 35. C2×C4×C7 | C23 | semidirect |
| 37. C2×Dic7 | C23 | semidirect |
| 44. C2×C22⋊C4 | D7 | direct (N × H) |
| 48. C22×C7 | C22×C4 | semidirect |
| 54. C2×D7 | C22⋊C4 | direct (N × H) |
| 56. C2×D7 | C22×C4 | semidirect |
| 69. C22×C4 | C2×D7 | semidirect |
| 72. C22⋊C4 | C2×D7 | direct (N × H) |
| 74. C2×C7 | C2×C22⋊C4 | semidirect |
| 78. D7 | C2×C22⋊C4 | direct (N × H) |
| 89. C23 | C4×D7 | semidirect |
| 96. C2×C4 | C22×D7 | semidirect |
| 97. C7 | C22×C22⋊C4 | semidirect |
| 108. C22 | C2×C4×D7 | semidirect |
| 116. C2 | D7×C22⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D7 | 2 |
| C22×C4×D7 | 2 |
| C2×C7×C22⋊C4 | 2 |
| C2×C22⋊Dic7 | 2 |
| C2×(C2×D7)⋊C4 | 2 |
| D7×C22⋊C4 | 2 |
| C22×C22⋊C4 | 7 |