Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
184 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 3. C3×C7×C4⋊C4 | C2 | semidirect |
| 4. C3×C4⋊Dic7 | C2 | semidirect |
| 5. C3×Dic7⋊C4 | C2 | semidirect |
| 6. D7×C4⋊C4 | C3 | direct (N × H) |
| 13. C3×C4×D7 | C4 | semidirect |
| 16. C7×C4⋊C4 | C2×C3 | semidirect |
| 17. C4⋊Dic7 | C2×C3 | semidirect |
| 18. Dic7⋊C4 | C2×C3 | semidirect |
| 25. C3×C4×C7 | C2×C4 | semidirect |
| 27. C3×Dic7 | C2×C4 | semidirect |
| 34. C4×D7 | C3×C4 | semidirect |
| 39. C3×C4⋊C4 | D7 | direct (N × H) |
| 43. C3×D7 | C4⋊C4 | direct (N × H) |
| 50. C4×C7 | C2×C3×C4 | semidirect |
| 52. Dic7 | C2×C3×C4 | semidirect |
| 60. C3×C7 | C2×C4⋊C4 | semidirect |
| 65. C4⋊C4 | C3×D7 | direct (N × H) |
| 69. D7 | C3×C4⋊C4 | direct (N × H) |
| 77. C3×C4 | C4×D7 | semidirect |
| 85. C7 | C2×C3×C4⋊C4 | semidirect |
| 97. C4 | C3×C4×D7 | semidirect |
| 98. C3 | D7×C4⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D7 | 2 |
| C3×C7×C4⋊C4 | 2 |
| C3×C4⋊Dic7 | 2 |
| C3×Dic7⋊C4 | 2 |
| D7×C4⋊C4 | 3 |
| C2×C3×C4⋊C4 | 7 |