Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1396 conjugacy classes of subgroups; only the 484 normal subgroups are shown.
This group has 1396 conjugacy classes of subgroups — too many to draw. Only its 484 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. C22⋊H(5,𝔽3) | C2 | direct (N × H) |
| 2. C23×C3×H(3,𝔽3) | C3 | semidirect |
| 3. C2×C3×C22⋊H(3,𝔽3) | C3 | semidirect |
| 4. C2×A4×H(3,𝔽3) | C3 | semidirect |
| 8. C22×C3×H(3,𝔽3) | C2×C3 | semidirect |
| 9. C3×C22⋊H(3,𝔽3) | C2×C3 | semidirect |
| 10. A4×H(3,𝔽3) | C2×C3 | semidirect |
| 12. C23×C33 | C32 | semidirect |
| 13. C2×C32×A4 | C32 | semidirect |
| 14. C23×H(3,𝔽3) | C32 | semidirect |
| 15. C2×C22⋊H(3,𝔽3) | C32 | semidirect |
| 16. C2×C22⋊H(3,𝔽3) | C32 | semidirect |
| 21. C2×C3×H(3,𝔽3) | A4 | semidirect |
| 24. C22×C33 | C2×C32 | semidirect |
| 25. C32×A4 | C2×C32 | semidirect |
| 28. C22×H(3,𝔽3) | C2×C32 | semidirect |
| 29. C22⋊H(3,𝔽3) | C2×C32 | semidirect |
| 30. C22⋊H(3,𝔽3) | C2×C32 | semidirect |
| 33. C3×H(3,𝔽3) | C2×A4 | semidirect |
| 42. C2×C33 | C3×A4 | semidirect |
| 47. C2×H(3,𝔽3) | C3×A4 | semidirect |
| 60. C33 | C2×C3×A4 | semidirect |
| 63. H(3,𝔽3) | C2×C3×A4 | semidirect |
| 94. C23 | H(5,𝔽3) | semidirect |
| 107. C22 | C2×H(5,𝔽3) | semidirect |
| 114. C2 | C22⋊H(5,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22⋊H(5,𝔽3) | 2 |
| C23×C3×H(3,𝔽3) | 3 |
| C2×C3×C22⋊H(3,𝔽3) | 3 |
| C2×A4×H(3,𝔽3) | 3 |
| C2×H(5,𝔽3) | 4 |