Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
136 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 41 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. #66732 | C2 | semidirect |
| 2. D4×D21 | C2 | semidirect |
| 3. C3×C7×SD16 | C2 | semidirect |
| 4. #66634 | C2 | semidirect |
| 5. #66632 | C2 | semidirect |
| 6. D168 | C2 | semidirect |
| 7. #66622 | C2 | semidirect |
| 10. C3×C7×Q8 | C22 | semidirect |
| 15. D84 | C22 | semidirect |
| 18. C3×C7×C8 | C22 | semidirect |
| 19. C3⋊(C7⋊C8) | C22 | semidirect |
| 22. C7×SD16 | D3 | semidirect |
| 37. C7×Q8 | C2×D3 | semidirect |
| 45. C7×C8 | C2×D3 | semidirect |
| 49. C3×SD16 | D7 | semidirect |
| 69. C3×Q8 | C2×D7 | semidirect |
| 77. C3×C8 | C2×D7 | semidirect |
| 79. C3×C7 | AGL(1,ℤ/8) | semidirect |
| 83. SD16 | D21 | semidirect |
| 101. Q8 | C2×D21 | semidirect |
| 110. C8 | C2×D21 | semidirect |
| 111. C7 | #914 | semidirect |
| 125. C3 | #6477 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66732 | 2 |
| D4×D21 | 2 |
| C3×C7×SD16 | 2 |
| #66634 | 2 |
| #66632 | 2 |
| D168 | 2 |
| #66622 | 2 |
| #6477 | 3 |
| #914 | 7 |