Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
313 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 313 conjugacy classes of subgroups — too many to draw. Only its 43 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. C3×C4⋊#272 | C2 | semidirect |
| 2. C4⋊(C3⋊((C3⋊D3)⋊C3)) | C2 | semidirect |
| 3. C3⋊((C3⋊(C3⋊C8))⋊C3) | C2 | semidirect |
| 10. C4⋊(C3⋊(C3⋊D3)) | D3 | semidirect |
| 15. C3⋊(C3⋊(C3⋊C8)) | D3 | semidirect |
| 17. C4⋊#272 | D3 | semidirect |
| 45. C3×H(3,𝔽3) | D8 | semidirect |
| 108. C33 | D24 | semidirect |
| 109. C33 | #213 | semidirect |
| 113. H(3,𝔽3) | #213 | semidirect |
| 178. C32 | #3713 | semidirect |
| 180. C32 | #3714 | semidirect |
| 211. C3 | #88436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4⋊#272 | 2 |
| C4⋊(C3⋊((C3⋊D3)⋊C3)) | 2 |
| C3⋊((C3⋊(C3⋊C8))⋊C3) | 2 |
| #88790 | 3 |
| #88789 | 3 |
| #88436 | 3 |