Finite Group DatabasebetaFinite Group DatabasebetaOrder 1008.
164 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 164 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. #92722 | C2 | semidirect |
| 2. C3×Dic42 | C2 | semidirect |
| 4. #92691 | C2 | semidirect |
| 19. Dic42 | D3 | direct (N × H) |
| 26. C3×D3×C7 | Q8 | semidirect |
| 45. C32×C7 | C2×Q8 | semidirect |
| 57. D3×C7 | Dic6 | semidirect |
| 80. C3×C7 | C2×Dic6 | semidirect |
| 81. C3×C7 | D3×Q8 | semidirect |
| 83. C3×D3 | Dic14 | semidirect |
| 99. C32 | C2×Dic14 | semidirect |
| 105. C7 | D3×Dic6 | semidirect |
| 110. D3 | Dic42 | direct (N × H) |
| 117. C3 | D3×Dic14 | semidirect |
| 118. C3 | C2×Dic42 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #92722 | 2 |
| C3×Dic42 | 2 |
| C3×C4×D3×C7 | 2 |
| #92691 | 2 |
| D3×Dic21 | 2 |
| C2×Dic42 | 3 |
| D3×Dic14 | 3 |
| D3×Dic6 | 7 |