Finite Group DatabasebetaFinite Group DatabasebetaOrder 38637.
476 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 476 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 |
| prime radical | C32×H(3,𝔽3)×C53 | C3 |
| 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 |
|---|---|---|
| 2. C53×#6891 | C3 | semidirect |
| 3. C3×C53×C32⋊C9 | C3 | semidirect |
| 4. C53×H(3,𝔽3)⋊C9 | C3 | semidirect |
| 11. C32×C9×C53 | C32 | semidirect |
| 16. C53×C32⋊C9 | C32 | semidirect |
| 32. H(3,𝔽3)×C53 | 3−1+2 | semidirect |
| 36. #10624778 | C53 | direct (N × H) |
| 59. #6891 | C3×C53 | semidirect |
| 60. C3×C32⋊C9 | C3×C53 | semidirect |
| 61. H(3,𝔽3)⋊C9 | C3×C53 | semidirect |
| 76. C32×C9 | C32×C53 | semidirect |
| 81. C32⋊C9 | C32×C53 | semidirect |
| 82. C53 | #10624778 | direct (N × H) |
| 98. H(3,𝔽3) | 3−1+2×C53 | 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 |
| C53×#6891 | 3 |
| C3×C53×C32⋊C9 | 3 |
| C53×H(3,𝔽3)⋊C9 | 3 |
| #10624778 | 53 |