Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
552 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 77 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. #10619988 | C2 | semidirect |
| 2. C3×C4×#272 | C2 | semidirect |
| 3. D12×H(3,𝔽3) | C2 | semidirect |
| 4. #10619891 | C2 | semidirect |
| 5. D3×#1084 | C2 | semidirect |
| 14. C32×D12 | D3 | semidirect |
| 21. C4×#272 | D3 | semidirect |
| 42. C3×H(3,𝔽3) | #41 | semidirect |
| 90. C33 | #237 | semidirect |
| 92. H(3,𝔽3) | #235 | semidirect |
| 104. D12 | #272 | semidirect |
| 146. C32 | #3795 | semidirect |
| 173. C3 | #88744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619988 | 2 |
| C3×C4×#272 | 2 |
| D12×H(3,𝔽3) | 2 |
| #10619891 | 2 |
| D3×#1084 | 2 |
| C3×#3795 | 3 |
| #88744 | 3 |