Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1815 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 1815 conjugacy classes of subgroups — too many to draw. Only its 261 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. H(3,𝔽3)×#95 | C2 | semidirect |
| 3. #11720574 | C2 | semidirect |
| 9. C2×C4×#272 | C4 | semidirect |
| 11. C32×#95 | D3 | semidirect |
| 18. C2×C4×H(3,𝔽3) | C2×C4 | semidirect |
| 20. C2×#1084 | C2×C4 | semidirect |
| 48. C2×C32×C4 | C4×D3 | semidirect |
| 56. #272 | #95 | direct (N × H) |
| 77. #95 | #272 | direct (N × H) |
| 78. H(3,𝔽3) | C2×#95 | semidirect |
| 122. C32 | D3×#95 | semidirect |
| 131. C2×C4 | C4×#272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#272 | 2 |
| H(3,𝔽3)×#95 | 2 |
| #11720574 | 2 |
| C3×D3×#95 | 3 |