Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 120 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 |
|---|---|---|
| 2. C3×Q8×D7 | C2 | semidirect |
| 3. C3×C7×Q16 | C2 | semidirect |
| 4. C3×#1144 | C2 | semidirect |
| 5. C3×#1143 | C2 | semidirect |
| 6. C3×#1132 | C2 | semidirect |
| 7. C3×#1131 | C2 | semidirect |
| 8. #6481 | C3 | direct (N × H) |
| 21. Q8×D7 | C2×C3 | semidirect |
| 22. C7×Q16 | C2×C3 | semidirect |
| 23. #1144 | C2×C3 | semidirect |
| 24. #1143 | C2×C3 | semidirect |
| 25. #1132 | C2×C3 | semidirect |
| 26. #1131 | C2×C3 | semidirect |
| 49. C3×Q16 | D7 | semidirect |
| 75. C3×C7 | #137 | semidirect |
| 79. Q16 | C3×D7 | semidirect |
| 104. C7 | C3×#137 | semidirect |
| 115. C3 | #6481 | 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×Q8×D7 | 2 |
| C3×C7×Q16 | 2 |
| C3×#1144 | 2 |
| C3×#1143 | 2 |
| C3×#1132 | 2 |
| C3×#1131 | 2 |
| #6481 | 3 |
| C3×#137 | 7 |