Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
156 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 62 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×C3×C4×D7 | C2 | semidirect |
| 3. C3×C7×C4⋊C4 | C2 | semidirect |
| 4. C3×(C2×D7)⋊C4 | C2 | semidirect |
| 5. C3×(C2×D7)⋊C4 | C2 | semidirect |
| 6. C3×(C2×D7)⋊C4 | C2 | semidirect |
| 7. C3×Dic7⋊C4 | C2 | semidirect |
| 8. #6457 | C3 | direct (N × H) |
| 19. C2×C4×D7 | C2×C3 | semidirect |
| 20. C7×C4⋊C4 | C2×C3 | semidirect |
| 21. (C2×D7)⋊C4 | C2×C3 | semidirect |
| 22. (C2×D7)⋊C4 | C2×C3 | semidirect |
| 23. (C2×D7)⋊C4 | C2×C3 | semidirect |
| 24. Dic7⋊C4 | C2×C3 | semidirect |
| 50. C3×C4⋊C4 | D7 | semidirect |
| 81. C3×C7 | #123 | semidirect |
| 85. C4⋊C4 | C3×D7 | semidirect |
| 115. C7 | C3×#123 | semidirect |
| 133. C3 | #6457 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D28 | 2 |
| C2×C3×C4×D7 | 2 |
| C3×C7×C4⋊C4 | 2 |
| C3×(C2×D7)⋊C4 | 2 |
| C3×Dic7⋊C4 | 2 |
| #6457 | 3 |
| C3×#123 | 7 |