Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
120 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 58 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. C2×C3×C7×Q8 | C2 | semidirect |
| 3. C3×#1144 | C2 | semidirect |
| 4. C3×#1143 | C2 | semidirect |
| 5. C3×#1136 | C2 | semidirect |
| 6. #6505 | C3 | direct (N × H) |
| 16. C2×C7×Q8 | C2×C3 | semidirect |
| 18. #1144 | C2×C3 | semidirect |
| 19. #1143 | C2×C3 | semidirect |
| 20. #1136 | C2×C3 | semidirect |
| 38. C2×C3×Q8 | D7 | semidirect |
| 61. C3×C7 | #137 | semidirect |
| 63. C2×Q8 | C3×D7 | semidirect |
| 85. C7 | C3×#137 | semidirect |
| 95. C3 | #6505 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×Q8 | 2 |
| C3×#1157 | 2 |
| C3×#1144 | 2 |
| C3×#1143 | 2 |
| C3×#1136 | 2 |
| #6505 | 3 |
| C3×#137 | 7 |