Finite Group DatabasebetaFinite Group Databasebeta← C2×C32×C22⋊H(3,𝔽3) #14519351
Order 1944.
2648 conjugacy classes of subgroups; only the 568 normal subgroups are shown.
This group has 2648 conjugacy classes of subgroups — too many to draw. Only its 568 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C33 | C3×A4 |
| commutator, cosocle | C22×C3 | C2×C34 |
| Frattini | C3 | C2×C33×A4 |
| Fitting | C23×C34 | C3 |
| socle | C23×C33 | C32 |
| hypercenter | C2×C34 | A4 |
| hypocenter | C22 | C2×C32×H(3,𝔽3) |
| LCS | G ▷ C22×C3 ▷ C22 | |
| UCS | C1 ◁ C2×C33 ◁ C2×C34 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C22⋊H(3,𝔽3) | C2 | direct (N × H) |
| 2. C23×C34 | C3 | semidirect |
| 3. C2×C33×A4 | C3 | semidirect |
| 4. C2×C3×C22⋊H(3,𝔽3) | C3 | direct (N × H) |
| 8. C22×C34 | C2×C3 | semidirect |
| 9. C33×A4 | C2×C3 | semidirect |
| 10. C3×C22⋊H(3,𝔽3) | C2×C3 | direct (N × H) |
| 14. C23×C33 | C32 | semidirect |
| 16. C2×C32×A4 | C32 | semidirect |
| 17. C2×C22⋊H(3,𝔽3) | C32 | direct (N × H) |
| 21. C2×C34 | A4 | semidirect |
| 31. C22×C33 | C2×C32 | semidirect |
| 33. C32×A4 | C2×C32 | semidirect |
| 34. C22⋊H(3,𝔽3) | C2×C32 | direct (N × H) |
| 36. C34 | C2×A4 | semidirect |
| 39. C23×C32 | H(3,𝔽3) | semidirect |
| 41. C23×C32 | C33 | semidirect |
| 43. C2×C3×A4 | C33 | semidirect |
| 54. C2×C33 | C3×A4 | semidirect |
| 65. C22×C32 | C2×H(3,𝔽3) | semidirect |
| 67. C22×C32 | C2×C33 | semidirect |
| 69. C3×A4 | C2×C33 | semidirect |
| 74. C33 | C2×C3×A4 | semidirect |
| 77. C23×C3 | C3×H(3,𝔽3) | semidirect |
| 91. C2×C32 | C22⋊H(3,𝔽3) | direct (N × H) |
| 93. C2×C32 | C32×A4 | semidirect |
| 101. C22×C3 | C2×C3×H(3,𝔽3) | semidirect |
| 107. C32 | C2×C22⋊H(3,𝔽3) | direct (N × H) |
| 109. C32 | C2×C32×A4 | semidirect |
| 110. C23 | C32×H(3,𝔽3) | semidirect |
| 119. C2×C3 | C3×C22⋊H(3,𝔽3) | direct (N × H) |
| 123. C22 | C2×C32×H(3,𝔽3) | semidirect |
| 126. C3 | C2×C3×C22⋊H(3,𝔽3) | direct (N × H) |
| 130. C2 | C32×C22⋊H(3,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C22⋊H(3,𝔽3) | 2 |
| C23×C34 | 3 |
| C2×C33×A4 | 3 |
| C2×C3×C22⋊H(3,𝔽3) | 3 |
| C2×C32×H(3,𝔽3) | 4 |