Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2016 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 2016 conjugacy classes of subgroups — too many to draw. Only its 407 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×C33×D8 | C2 | semidirect |
| 2. #11723981 | C2 | semidirect |
| 3. #11723977 | C2 | semidirect |
| 4. C2×#88861 | C2 | semidirect |
| 5. C2×#88860 | C2 | semidirect |
| 6. C2×#88851 | C2 | semidirect |
| 7. #11722185 | C2 | semidirect |
| 22. C2×C32×D8 | D3 | semidirect |
| 44. C33×C8 | D4 | semidirect |
| 45. C3⋊(C3⋊(C3⋊C8)) | D4 | semidirect |
| 71. C2×C3×D8 | C3⋊D3 | semidirect |
| 93. C32×C8 | #67 | semidirect |
| 128. C2×D8 | C3⋊(C3⋊D3) | semidirect |
| 132. C33 | #496 | semidirect |
| 148. C3×C8 | #638 | semidirect |
| 179. C32 | #5154 | semidirect |
| 196. C8 | #6312 | semidirect |
| 213. C3 | #10592853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D8 | 2 |
| #11723981 | 2 |
| #11723977 | 2 |
| C2×#88861 | 2 |
| C2×#88860 | 2 |
| C2×#88851 | 2 |
| #11722185 | 2 |
| #10592853 | 3 |