Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
672 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C32 | C22×H(3,𝔽3) |
| commutator, Frattini, cosocle | C2×C32 | C22×C33 |
| LCS | G ▷ C2×C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C32 ◁ C33×D4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C3×#732 | C2 | semidirect |
| 2. C3×C4×#732 | C2 | semidirect |
| 3. C3×D4×H(3,𝔽3) | C3 | semidirect |
| 4. C32×D4×C9 | C3 | semidirect |
| 5. D4×#732 | C3 | direct (N × H) |
| 8. C22×C3×H(3,𝔽3) | C2×C3 | semidirect |
| 9. C22×C32×C9 | C2×C3 | semidirect |
| 10. C3×C4×H(3,𝔽3) | C2×C3 | semidirect |
| 11. C32×C4×C9 | C2×C3 | semidirect |
| 12. C22×#732 | C2×C3 | semidirect |
| 13. C4×#732 | C2×C3 | semidirect |
| 14. C3×#732 | D4 | direct (N × H) |
| 18. D4×H(3,𝔽3) | C32 | semidirect |
| 21. C3×D4×C9 | C32 | semidirect |
| 33. C22×H(3,𝔽3) | C2×C32 | semidirect |
| 36. C22×C3×C9 | C2×C32 | semidirect |
| 38. C4×H(3,𝔽3) | C2×C32 | semidirect |
| 41. C3×C4×C9 | C2×C32 | semidirect |
| 42. C3×H(3,𝔽3) | C3×D4 | semidirect |
| 43. C32×C9 | C3×D4 | semidirect |
| 44. #732 | C3×D4 | direct (N × H) |
| 83. H(3,𝔽3) | C32×D4 | semidirect |
| 86. C3×C9 | C32×D4 | semidirect |
| 90. C3×D4 | #732 | direct (N × H) |
| 109. C22×C3 | C2×#732 | semidirect |
| 114. C3×C4 | C2×#732 | semidirect |
| 123. D4 | C3×#732 | direct (N × H) |
| 134. C22 | C2×C3×#732 | semidirect |
| 135. C4 | C2×C3×#732 | semidirect |
| 139. C3 | D4×#732 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#732 | 2 |
| C3×C4×#732 | 2 |
| C3×D4×H(3,𝔽3) | 3 |
| C32×D4×C9 | 3 |
| D4×#732 | 3 |