Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
152 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 66 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×D28 | C2 | semidirect |
| 3. C3×#1141 | C2 | direct (N × H) |
| 4. C2×C3×C7⋊C8 | C2 | semidirect |
| 5. C2×#1141 | C3 | direct (N × H) |
| 9. C3×C7×D4 | C22 | semidirect |
| 12. C3×D28 | C22 | semidirect |
| 13. C3×C7⋊C8 | C22 | semidirect |
| 14. C2×C7×D4 | C2×C3 | semidirect |
| 15. C2×D28 | C2×C3 | semidirect |
| 16. #1141 | C2×C3 | direct (N × H) |
| 17. C2×C7⋊C8 | C2×C3 | semidirect |
| 29. C7×D4 | C22×C3 | semidirect |
| 32. D28 | C22×C3 | semidirect |
| 33. C7⋊C8 | C22×C3 | semidirect |
| 35. C2×C3×D4 | D7 | semidirect |
| 39. C2×C3×C7 | D8 | semidirect |
| 55. C3×D4 | C2×D7 | semidirect |
| 58. C3×C7 | C2×D8 | semidirect |
| 60. C2×D4 | C3×D7 | semidirect |
| 64. C2×C7 | C3×D8 | semidirect |
| 79. D4 | C2×C3×D7 | semidirect |
| 82. C7 | C2×C3×D8 | semidirect |
| 85. C2×C3 | #1141 | direct (N × H) |
| 94. C3 | C2×#1141 | direct (N × H) |
| 97. C2 | C3×#1141 | 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×D28 | 2 |
| C3×#1141 | 2 |
| C2×C3×C7⋊C8 | 2 |
| C2×#1141 | 3 |
| C2×C3×D8 | 7 |