Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1604 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 1604 conjugacy classes of subgroups — too many to draw. Only its 136 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. #11757866 | C2 | direct (N × H) |
| 2. C23×C34 | C3 | semidirect |
| 3. C2×C3×C22⋊H(3,𝔽3) | C3 | semidirect |
| 7. C22×C34 | C2×C3 | semidirect |
| 8. C3×C22⋊H(3,𝔽3) | C2×C3 | semidirect |
| 12. C2×C32×A4 | C32 | semidirect |
| 16. C2×C34 | A4 | semidirect |
| 24. C32×A4 | C2×C32 | semidirect |
| 26. C34 | C2×A4 | semidirect |
| 30. C23×C32 | H(3,𝔽3) | semidirect |
| 51. C22×C32 | C2×H(3,𝔽3) | semidirect |
| 72. C2×C32 | C22⋊H(3,𝔽3) | semidirect |
| 84. C32 | C2×C22⋊H(3,𝔽3) | semidirect |
| 86. C23 | C32⋊H(3,𝔽3) | semidirect |
| 96. C22 | C2×C32⋊H(3,𝔽3) | semidirect |
| 102. C2 | #11757866 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757866 | 2 |
| C23×C34 | 3 |
| C2×C3×C22⋊H(3,𝔽3) | 3 |
| C2×C32⋊H(3,𝔽3) | 4 |