Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
904 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 904 conjugacy classes of subgroups — too many to draw. Only its 238 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×C3×#3746 | C2 | semidirect |
| 4. C3×#64078 | C2 | semidirect |
| 5. C33×#97 | C2 | semidirect |
| 6. #10592414 | C3 | direct (N × H) |
| 17. C2×#3746 | C2×C3 | semidirect |
| 20. #64078 | C2×C3 | semidirect |
| 26. C32×#97 | D3 | semidirect |
| 27. C32×#97 | C2×C3 | semidirect |
| 76. C3×#97 | C3×D3 | semidirect |
| 77. C3×#97 | C3⋊D3 | semidirect |
| 146. #97 | C3×C3⋊D3 | semidirect |
| 147. C33 | #497 | semidirect |
| 206. C32 | #4715 | semidirect |
| 207. C32 | C3×#497 | semidirect |
| 234. C3 | C3×#4715 | semidirect |
| 235. C3 | #10592414 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3746 | 2 |
| C2×C3×#3744 | 2 |
| C3×#64084 | 2 |
| C3×#64078 | 2 |
| C33×#97 | 2 |
| #10592414 | 3 |
| C3×#4715 | 3 |