Finite Group DatabasebetaFinite Group DatabasebetaOrder 4374.
6154 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 6154 conjugacy classes of subgroups — too many to draw. Only its 237 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. C32⋊H(5,𝔽3) | C2 | semidirect |
| 2. C3×#92392 | C3 | semidirect |
| 3. C33×#272 | C3 | semidirect |
| 4. H(3,𝔽3)×#272 | C3 | semidirect |
| 6. C3×H(5,𝔽3) | C2×C3 | semidirect |
| 7. C33×H(3,𝔽3) | C2×C3 | semidirect |
| 9. H(3,𝔽3)2 | C2×C3 | semidirect |
| 12. C3×C32⋊H(3,𝔽3) | D3 | semidirect |
| 17. C32×#272 | C32 | semidirect |
| 18. C32×#272 | C32 | semidirect |
| 22. C35 | C3×D3 | semidirect |
| 32. C32×H(3,𝔽3) | C3×D3 | semidirect |
| 33. C32×H(3,𝔽3) | C3×D3 | semidirect |
| 36. C32×H(3,𝔽3) | C2×C32 | semidirect |
| 56. C3×#272 | H(3,𝔽3) | semidirect |
| 68. C34 | C32×D3 | semidirect |
| 97. C3×H(3,𝔽3) | C2×H(3,𝔽3) | semidirect |
| 117. #272 | C3×H(3,𝔽3) | semidirect |
| 141. C33 | D3×H(3,𝔽3) | semidirect |
| 203. C32 | #92392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32⋊H(5,𝔽3) | 2 |
| C3×#92392 | 3 |
| C33×#272 | 3 |
| H(3,𝔽3)×#272 | 3 |
| D3×C32⋊H(3,𝔽3) | 3 |