Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
124 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 54 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. C7×#239 | C2 | semidirect |
| 2. C7×#237 | C2 | semidirect |
| 3. C3×C7×SD16 | C2 | semidirect |
| 4. C7×#216 | C2 | semidirect |
| 5. C7×#213 | C2 | semidirect |
| 6. C7×#204 | C2 | semidirect |
| 7. D3×C7×C8 | C2 | semidirect |
| 24. C7×SD16 | D3 | semidirect |
| 27. #916 | C7 | direct (N × H) |
| 46. #239 | C2×C7 | semidirect |
| 47. #237 | C2×C7 | semidirect |
| 48. C3×SD16 | C2×C7 | semidirect |
| 49. #216 | C2×C7 | semidirect |
| 50. #213 | C2×C7 | semidirect |
| 51. #204 | C2×C7 | semidirect |
| 52. D3×C8 | C2×C7 | semidirect |
| 76. C3×C7 | #135 | semidirect |
| 81. SD16 | D3×C7 | semidirect |
| 106. C7 | #916 | direct (N × H) |
| 118. C3 | C7×#135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#239 | 2 |
| C7×#237 | 2 |
| C3×C7×SD16 | 2 |
| C7×#216 | 2 |
| C7×#213 | 2 |
| C7×#204 | 2 |
| D3×C7×C8 | 2 |
| C7×#135 | 3 |
| #916 | 7 |