Finite Group DatabasebetaFinite Group DatabasebetaOrder 38637.
306 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 80 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 | C53×#6856 | C3 |
| LCS | G ▷ C33 ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C53 ◁ C32×C9×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C53×#737 | C3 | semidirect |
| 2. C53×#6894 | C3 | semidirect |
| 3. C53×C9⋊H(3,𝔽3) | C3 | semidirect |
| 4. C53×#6860 | C3 | semidirect |
| 5. C53×#6859 | C3 | semidirect |
| 6. C53×#6858 | C3 | semidirect |
| 7. C53×#6857 | C3 | semidirect |
| 8. C53×#6857 | C3 | semidirect |
| 45. #10624634 | C53 | direct (N × H) |
| 64. C3×#737 | C3×C53 | semidirect |
| 65. #6894 | C3×C53 | semidirect |
| 66. C9⋊H(3,𝔽3) | C3×C53 | semidirect |
| 67. #6860 | C3×C53 | semidirect |
| 68. #6859 | C3×C53 | semidirect |
| 69. #6858 | C3×C53 | semidirect |
| 70. #6857 | C3×C53 | semidirect |
| 71. #6857 | C3×C53 | semidirect |
| 95. C53 | #10624634 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C53×#737 | 3 |
| C53×#6894 | 3 |
| C53×C9⋊H(3,𝔽3) | 3 |
| C53×#6860 | 3 |
| C53×#6859 | 3 |
| C53×#6858 | 3 |
| C53×#6857 | 3 |
| C53×#6856 | 3 |
| #10624634 | 53 |