Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
984 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 253 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. Q8×C3⋊#157 | C2 | direct (N × H) |
| 8. C2×C33×Q8 | C4 | semidirect |
| 9. C3×Q8×C3⋊D3 | C4 | semidirect |
| 12. C2×C3×#634 | C4 | semidirect |
| 22. C2×C3⋊#157 | Q8 | direct (N × H) |
| 25. C33×Q8 | C2×C4 | semidirect |
| 30. C3×#634 | C2×C4 | semidirect |
| 36. C2×C32×Q8 | Dic3 | semidirect |
| 37. Q8×C3⋊D3 | Dic3 | semidirect |
| 40. C2×#634 | Dic3 | semidirect |
| 53. C3⋊#157 | C2×Q8 | direct (N × H) |
| 69. C32×Q8 | C2×Dic3 | semidirect |
| 76. #634 | C2×Dic3 | semidirect |
| 82. C2×C33 | C4×Q8 | semidirect |
| 84. C3×C3⋊D3 | C4×Q8 | semidirect |
| 92. C2×C3×Q8 | #157 | semidirect |
| 124. C33 | C2×C4×Q8 | semidirect |
| 130. C3×Q8 | C2×#157 | semidirect |
| 149. C2×C32 | Q8×Dic3 | semidirect |
| 151. C3⋊D3 | Q8×Dic3 | semidirect |
| 160. C2×Q8 | C3⋊#157 | direct (N × H) |
| 186. C32 | C2×Q8×Dic3 | semidirect |
| 189. Q8 | C2×C3⋊#157 | direct (N × H) |
| 205. C2×C3 | Q8×#157 | semidirect |
| 221. C3 | C2×Q8×#157 | semidirect |
| 225. C2 | Q8×C3⋊#157 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q8×C3⋊D3 | 2 |
| Q8×C3⋊#157 | 2 |
| C2×C4⋊(C3⋊#157) | 2 |
| C2×C4×C3⋊#157 | 2 |
| C2×Q8×#157 | 3 |
| C2×Q8×Dic3 | 9 |