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×C4×D7 | C2 | semidirect |
| 4. C3×C22⋊Dic7 | C2 | semidirect |
| 5. C3×C4⋊Dic7 | C2 | semidirect |
| 6. #6501 | C3 | direct (N × H) |
| 15. C2×C7×D4 | C2×C3 | semidirect |
| 16. C2×C22⋊D7 | C2×C3 | semidirect |
| 17. C2×C4×D7 | C2×C3 | semidirect |
| 18. C22⋊Dic7 | C2×C3 | semidirect |
| 19. C4⋊Dic7 | C2×C3 | semidirect |
| 27. C2×C3×D7 | D4 | semidirect |
| 28. C3×C4×C7 | D4 | semidirect |
| 40. C2×C3×D4 | D7 | semidirect |
| 56. C2×D7 | C3×D4 | semidirect |
| 57. C4×C7 | C3×D4 | semidirect |
| 68. C3×C7 | #121 | semidirect |
| 70. C2×D4 | C3×D7 | semidirect |
| 88. C3×C4 | C22⋊D7 | semidirect |
| 97. C7 | C3×#121 | semidirect |
| 112. C4 | C3×C22⋊D7 | semidirect |
| 113. C3 | #6501 | 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 |
| C2×C3×C4×D7 | 2 |
| C3×C22⋊Dic7 | 2 |
| C3×C4⋊Dic7 | 2 |
| #6501 | 3 |
| C3×#121 | 7 |