Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
566 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 566 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. C4×C3⋊#272 | C2 | semidirect |
| 2. C3×#6229 | C2 | semidirect |
| 3. D12×H(3,𝔽3) | C2 | semidirect |
| 4. #10619892 | C2 | semidirect |
| 5. D3×#1084 | C2 | semidirect |
| 14. C32×D12 | D3 | semidirect |
| 23. #6229 | D3 | semidirect |
| 43. C3×H(3,𝔽3) | #41 | semidirect |
| 92. C33 | #237 | semidirect |
| 94. H(3,𝔽3) | #239 | semidirect |
| 106. D12 | #272 | semidirect |
| 148. C32 | #3796 | semidirect |
| 175. C3 | #88744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C3⋊#272 | 2 |
| C3×#6229 | 2 |
| D12×H(3,𝔽3) | 2 |
| #10619892 | 2 |
| D3×#1084 | 2 |
| C3×#3796 | 3 |
| #88744 | 3 |