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. C3×#1161 | C2 | semidirect |
| 2. C3×#1159 | C2 | semidirect |
| 3. C3×C7×SD16 | C2 | semidirect |
| 4. C3×#1144 | C2 | semidirect |
| 5. C3×#1141 | C2 | semidirect |
| 6. C3×#1132 | C2 | semidirect |
| 7. C3×C8×D7 | C2 | semidirect |
| 8. #6479 | C3 | direct (N × H) |
| 20. #1161 | C2×C3 | semidirect |
| 21. #1159 | C2×C3 | semidirect |
| 22. C7×SD16 | C2×C3 | semidirect |
| 23. #1144 | C2×C3 | semidirect |
| 24. #1141 | C2×C3 | semidirect |
| 25. #1132 | C2×C3 | semidirect |
| 26. C8×D7 | C2×C3 | semidirect |
| 50. C3×SD16 | D7 | semidirect |
| 76. C3×C7 | #135 | semidirect |
| 81. SD16 | C3×D7 | semidirect |
| 106. C7 | C3×#135 | semidirect |
| 118. C3 | #6479 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#1161 | 2 |
| C3×#1159 | 2 |
| C3×C7×SD16 | 2 |
| C3×#1144 | 2 |
| C3×#1141 | 2 |
| C3×#1132 | 2 |
| C3×C8×D7 | 2 |
| #6479 | 3 |
| C3×#135 | 7 |