Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
426 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 183 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×C42×C7 | C2 | semidirect |
| 4. C2×(C2×D7)⋊C4 | C2 | semidirect |
| 5. C2×C4⋊Dic7 | C2 | semidirect |
| 6. C4×D28 | C2 | direct (N × H) |
| 12. C2×D28 | C4 | direct (N × H) |
| 15. C2×C4×D7 | C22 | semidirect |
| 16. C42×C7 | C22 | semidirect |
| 17. (C2×D7)⋊C4 | C22 | semidirect |
| 18. C4⋊Dic7 | C22 | semidirect |
| 23. C22×D7 | C2×C4 | semidirect |
| 26. C2×C4×C7 | C2×C4 | semidirect |
| 27. C2×C4×C7 | D4 | semidirect |
| 33. D28 | C2×C4 | direct (N × H) |
| 40. C2×C42 | D7 | semidirect |
| 48. C2×D7 | C22×C4 | semidirect |
| 50. C4×C7 | C22×C4 | semidirect |
| 51. C4×C7 | C2×D4 | semidirect |
| 64. C42 | C2×D7 | semidirect |
| 65. C2×C7 | C4×D4 | semidirect |
| 80. C2×C4 | C4×D7 | semidirect |
| 81. C2×C4 | D28 | direct (N × H) |
| 85. C7 | C2×C4×D4 | semidirect |
| 96. C4 | C2×C4×D7 | semidirect |
| 97. C4 | C2×D28 | direct (N × H) |
| 99. C2 | C4×D28 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D28 | 2 |
| C22×C4×D7 | 2 |
| C2×C42×C7 | 2 |
| C2×(C2×D7)⋊C4 | 2 |
| C2×C4⋊Dic7 | 2 |
| C4×D28 | 2 |
| C2×C4×D4 | 7 |