Finite Group DatabasebetaFinite Group DatabasebetaOrder 5184.
781 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 781 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×PSU(3,𝔽2)⋊C3 | C2 | semidirect |
| 2. C2×C3⋊AGL(2,𝔽3) | C2 | semidirect |
| 10. C3×C4×PSU(3,𝔽2) | D3 | semidirect |
| 14. C4×PSU(3,𝔽2)⋊C3 | D3 | semidirect |
| 15. C3×PSU(3,𝔽2)⋊C3 | D4 | semidirect |
| 45. C4×PSU(3,𝔽2) | C3⋊D3 | semidirect |
| 55. C3×PSU(3,𝔽2) | D12 | semidirect |
| 60. PSU(3,𝔽2)⋊C3 | D12 | semidirect |
| 111. C33×C4 | GL(2,𝔽3) | semidirect |
| 112. C3×C3⋊Dic3 | GL(2,𝔽3) | semidirect |
| 138. PSU(3,𝔽2) | C4⋊(C3⋊D3) | semidirect |
| 230. C32×C4 | C3⋊GL(2,𝔽3) | semidirect |
| 231. C3⋊Dic3 | C3⋊GL(2,𝔽3) | semidirect |
| 241. C33 | C4⋊GL(2,𝔽3) | semidirect |
| 331. C3×C4 | AGL(2,𝔽3) | semidirect |
| 341. C32 | C4⋊(C3⋊GL(2,𝔽3)) | semidirect |
| 380. C4 | C3⋊AGL(2,𝔽3) | semidirect |
| 385. C3 | C4⋊AGL(2,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×PSU(3,𝔽2)⋊C3 | 2 |
| C2×C3⋊AGL(2,𝔽3) | 2 |
| #13180419 | 3 |
| C4⋊AGL(2,𝔽3) | 3 |
| #13048679 | 4 |
| C4⋊(C3⋊GL(2,𝔽3)) | 9 |