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 |
|---|---|---|
| 2. C2×C3×Dic14 | C2 | semidirect |
| 3. C3×C7×M16 | C2 | semidirect |
| 4. C3×Dic28 | C2 | semidirect |
| 5. C3×#1132 | C2 | semidirect |
| 6. #6472 | C3 | direct (N × H) |
| 17. C2×Dic14 | C2×C3 | semidirect |
| 18. C7×M16 | C2×C3 | semidirect |
| 19. Dic28 | C2×C3 | semidirect |
| 20. #1132 | C2×C3 | semidirect |
| 41. C3×M16 | D7 | semidirect |
| 61. C3×C7 | #137 | semidirect |
| 66. M16 | C3×D7 | semidirect |
| 85. C7 | C3×#137 | semidirect |
| 95. C3 | #6472 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#1157 | 2 |
| C2×C3×Dic14 | 2 |
| C3×C7×M16 | 2 |
| C3×Dic28 | 2 |
| C3×#1132 | 2 |
| #6472 | 3 |
| C3×#137 | 7 |