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 |
|---|---|---|
| 1. C23×C4×C7 | C2 | semidirect |
| 3. C22×C4×D7 | C2 | semidirect |
| 4. C2×C22⋊Dic7 | C2 | semidirect |
| 5. C4×C22⋊D7 | C2 | direct (N × H) |
| 6. C2×(C2×D7)⋊C4 | C2 | semidirect |
| 7. C2×Dic7⋊C4 | C2 | semidirect |
| 8. C2×C4×Dic7 | C2 | semidirect |
| 14. C22×C4×C7 | C22 | semidirect |
| 15. C2×C22⋊D7 | C4 | direct (N × H) |
| 21. C2×C4×D7 | C22 | semidirect |
| 22. C22⋊Dic7 | C22 | semidirect |
| 23. (C2×D7)⋊C4 | C22 | semidirect |
| 24. Dic7⋊C4 | C22 | semidirect |
| 25. C4×Dic7 | C22 | semidirect |
| 29. C23×C7 | C2×C4 | semidirect |
| 34. C22×D7 | C2×C4 | semidirect |
| 38. C2×C4×C7 | D4 | semidirect |
| 41. C22⋊D7 | C2×C4 | direct (N × H) |
| 44. C2×Dic7 | C2×C4 | semidirect |
| 51. C23×C4 | D7 | semidirect |
| 61. C22×C7 | C22×C4 | semidirect |
| 68. C2×D7 | C22×C4 | semidirect |
| 70. C4×C7 | C2×D4 | semidirect |
| 73. Dic7 | C22×C4 | semidirect |
| 86. C22×C4 | C2×D7 | semidirect |
| 92. C2×C7 | C4×D4 | semidirect |
| 103. C23 | C4×D7 | semidirect |
| 116. C2×C4 | C22⋊D7 | direct (N × H) |
| 119. C7 | C2×C4×D4 | semidirect |
| 128. C22 | C2×C4×D7 | semidirect |
| 136. C4 | C2×C22⋊D7 | direct (N × H) |
| 139. C2 | C4×C22⋊D7 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C7 | 2 |
| C22×C22⋊D7 | 2 |
| C22×C4×D7 | 2 |
| C2×C22⋊Dic7 | 2 |
| C4×C22⋊D7 | 2 |
| C2×(C2×D7)⋊C4 | 2 |
| C2×Dic7⋊C4 | 2 |
| C2×C4×Dic7 | 2 |
| C2×C4×D4 | 7 |