Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
188 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 70 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. C2×C3×C7×D4 | C2 | semidirect |
| 2. C2×C3×C22⋊D7 | C2 | semidirect |
| 3. C2×C3×C22⋊D7 | C2 | semidirect |
| 4. C22×C3×Dic7 | C2 | semidirect |
| 5. C3×C22⋊Dic7 | C2 | semidirect |
| 6. C3×(C2×D7)⋊C4 | C2 | semidirect |
| 7. C3×Dic7⋊C4 | C2 | semidirect |
| 8. #6502 | C3 | direct (N × H) |
| 20. C2×C7×D4 | C2×C3 | semidirect |
| 21. C2×C22⋊D7 | C2×C3 | semidirect |
| 22. C2×C22⋊D7 | C2×C3 | semidirect |
| 23. C22×Dic7 | C2×C3 | semidirect |
| 24. C22⋊Dic7 | C2×C3 | semidirect |
| 25. (C2×D7)⋊C4 | C2×C3 | semidirect |
| 26. Dic7⋊C4 | C2×C3 | semidirect |
| 33. C22×C3×C7 | D4 | semidirect |
| 41. C3×Dic7 | D4 | semidirect |
| 55. C2×C3×D4 | D7 | semidirect |
| 72. C22×C7 | C3×D4 | semidirect |
| 80. Dic7 | C3×D4 | semidirect |
| 92. C3×C7 | #121 | semidirect |
| 95. C2×D4 | C3×D7 | semidirect |
| 114. C22×C3 | C22⋊D7 | semidirect |
| 131. C7 | C3×#121 | semidirect |
| 146. C22 | C3×C22⋊D7 | semidirect |
| 152. C3 | #6502 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×D4 | 2 |
| C2×C3×C22⋊D7 | 2 |
| C22×C3×Dic7 | 2 |
| C3×C22⋊Dic7 | 2 |
| C3×(C2×D7)⋊C4 | 2 |
| C3×Dic7⋊C4 | 2 |
| #6502 | 3 |
| C3×#121 | 7 |