Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1624 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 1624 conjugacy classes of subgroups — too many to draw. Only its 192 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. C2×C32×#272 | C2 | semidirect |
| 2. C32×C4×H(3,𝔽3) | C2 | semidirect |
| 4. C3×C4⋊#272 | C3 | direct (N × H) |
| 8. C34×C4 | D3 | semidirect |
| 9. C2×C3×#272 | C2×C3 | semidirect |
| 11. C3×C4×H(3,𝔽3) | C2×C3 | semidirect |
| 12. C32×H(3,𝔽3) | D4 | semidirect |
| 16. C4⋊#272 | C32 | direct (N × H) |
| 27. C33×C4 | C3×D3 | semidirect |
| 29. C2×#272 | C2×C32 | semidirect |
| 32. C4×H(3,𝔽3) | C2×C32 | semidirect |
| 33. C34 | D12 | semidirect |
| 35. C3×H(3,𝔽3) | C3×D4 | semidirect |
| 58. C32×C4 | #272 | semidirect |
| 59. C32×C4 | C32×D3 | semidirect |
| 63. C33 | C3×D12 | semidirect |
| 67. H(3,𝔽3) | C32×D4 | semidirect |
| 86. C3×C4 | C3×#272 | semidirect |
| 91. C32 | C4⋊#272 | direct (N × H) |
| 92. C32 | C32×D12 | semidirect |
| 103. C4 | C32×#272 | semidirect |
| 106. C3 | C3×C4⋊#272 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#272 | 2 |
| C32×C4×H(3,𝔽3) | 2 |
| C33×D12 | 3 |
| C3×C4⋊#272 | 3 |