Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
120 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 58 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. C3×C7×C4⋊C4 | C2 | semidirect |
| 5. C3×C4⋊Dic7 | C2 | semidirect |
| 6. C3×Dic7⋊C4 | C2 | semidirect |
| 7. C3×C4×Dic7 | C2 | semidirect |
| 8. #6461 | C3 | direct (N × H) |
| 16. C7×C4⋊C4 | C2×C3 | semidirect |
| 20. C4⋊Dic7 | C2×C3 | semidirect |
| 21. Dic7⋊C4 | C2×C3 | semidirect |
| 22. C4×Dic7 | C2×C3 | semidirect |
| 43. C3×C4⋊C4 | D7 | semidirect |
| 70. C3×C7 | #126 | semidirect |
| 73. C4⋊C4 | C3×D7 | semidirect |
| 99. C7 | C3×#126 | semidirect |
| 114. C3 | #6461 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×C4⋊C4 | 2 |
| C3×(C2×D7)⋊C4 | 2 |
| C3×C4⋊Dic7 | 2 |
| C3×Dic7⋊C4 | 2 |
| C3×C4×Dic7 | 2 |
| #6461 | 3 |
| C3×#126 | 7 |