Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2268 conjugacy classes of subgroups; only the 1075 normal subgroups are shown.
This group has 2268 conjugacy classes of subgroups — too many to draw. Only its 1075 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 |
|---|---|---|
| 4. #11722205 | C2 | direct (N × H) |
| 8. C2×C33×Q8 | C4 | semidirect |
| 24. C33×Q8 | C2×C4 | semidirect |
| 37. C2×C32×Q8 | Dic3 | semidirect |
| 62. C32×Q8 | C2×Dic3 | semidirect |
| 73. C2×C33 | #103 | semidirect |
| 79. C2×C3×Q8 | C3⋊Dic3 | semidirect |
| 101. C33 | C2×#103 | semidirect |
| 105. C3×Q8 | C2×C3⋊Dic3 | semidirect |
| 115. C2×C32 | #835 | semidirect |
| 121. C2×Q8 | C3⋊(C3⋊Dic3) | semidirect |
| 139. C32 | C2×#835 | semidirect |
| 143. Q8 | C2×C3⋊(C3⋊Dic3) | semidirect |
| 153. C2×C3 | #63662 | semidirect |
| 166. C3 | C2×#63662 | semidirect |
| 167. C2 | #11722205 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×Q8 | 2 |
| C2×C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| C22×C3⋊(C3⋊(C3⋊C8)) | 2 |
| #11722205 | 2 |
| C2×#63662 | 3 |