Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 3. #11723094 | C2 | direct (N × H) |
| 9. C2×C33×C8 | C4 | semidirect |
| 10. C2×C3×C3⋊(C3⋊C8) | C4 | semidirect |
| 11. C3×C8×C3⋊D3 | C4 | semidirect |
| 26. C33×C8 | C2×C4 | semidirect |
| 27. C3×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 36. C2×C32×C8 | Dic3 | semidirect |
| 37. C2×C3⋊(C3⋊C8) | Dic3 | semidirect |
| 38. C8×C3⋊D3 | Dic3 | semidirect |
| 76. C32×C8 | C2×Dic3 | semidirect |
| 77. C3⋊(C3⋊C8) | C2×Dic3 | semidirect |
| 80. C2×C33 | #107 | semidirect |
| 82. C3×C3⋊D3 | #107 | semidirect |
| 93. C2×C3×C8 | #157 | semidirect |
| 124. C33 | C2×#107 | semidirect |
| 145. C3×C8 | C2×#157 | semidirect |
| 151. C2×C32 | #818 | semidirect |
| 153. C3⋊D3 | #818 | semidirect |
| 164. C2×C8 | C3⋊#157 | semidirect |
| 191. C32 | C2×#818 | semidirect |
| 202. C8 | C2×C3⋊#157 | semidirect |
| 210. C2×C3 | #63769 | semidirect |
| 227. C3 | C2×#63769 | semidirect |
| 231. C2 | #11723094 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊#157) | 2 |
| C2×C3×C8×C3⋊D3 | 2 |
| #11723094 | 2 |
| C2×#63769 | 3 |
| C2×#818 | 9 |