Finite Group DatabasebetaFinite Group DatabasebetaOrder 38637.
650 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C53 | C3×H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C33×C53 |
| LCS | G ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C53 ◁ C34×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×H(3,𝔽3)×C53 | C3 | semidirect |
| 2. C3×C53×#732 | C3 | semidirect |
| 3. C53×C32⋊H(3,𝔽3) | C3 | semidirect |
| 4. C3×C53×C32⋊C9 | C3 | semidirect |
| 12. C3×H(3,𝔽3)×C53 | C32 | semidirect |
| 13. C32×C9×C53 | C32 | semidirect |
| 33. H(3,𝔽3)×C53 | H(3,𝔽3) | semidirect |
| 36. #10624740 | C53 | direct (N × H) |
| 52. C32×C53 | #732 | semidirect |
| 56. C32×H(3,𝔽3) | C3×C53 | semidirect |
| 57. C3×#732 | C3×C53 | semidirect |
| 58. C32⋊H(3,𝔽3) | C3×C53 | semidirect |
| 59. C3×C32⋊C9 | C3×C53 | semidirect |
| 75. C3×H(3,𝔽3) | C32×C53 | semidirect |
| 76. C32×C9 | C32×C53 | semidirect |
| 80. C53 | #10624740 | direct (N × H) |
| 97. H(3,𝔽3) | H(3,𝔽3)×C53 | semidirect |
| 115. C32 | C53×#732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×H(3,𝔽3)×C53 | 3 |
| C3×C53×#732 | 3 |
| C53×C32⋊H(3,𝔽3) | 3 |
| C3×C53×C32⋊C9 | 3 |
| #10624740 | 53 |