Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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. #66635 | C2 | semidirect |
| 4. C7×#216 | C2 | semidirect |
| 5. #66570 | C2 | semidirect |
| 6. #66569 | C2 | semidirect |
| 51. #216 | D7 | direct (N × H) |
| 54. C3×D7 | Q16 | semidirect |
| 74. C3×C7 | C2×Q16 | semidirect |
| 83. D7 | #216 | direct (N × H) |
| 102. C7 | C2×#216 | semidirect |
| 112. C3 | D7×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×D7 | 2 |
| D7×Dic6 | 2 |
| #66635 | 2 |
| C7×#216 | 2 |
| #66570 | 2 |
| #66569 | 2 |
| D7×C3⋊C8 | 2 |
| D7×Q16 | 3 |
| C2×#216 | 7 |