Finite Group DatabasebetaFinite Group DatabasebetaOrder 38637.
224 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 74 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 ▷ 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. C53×#6895 | C3 | semidirect |
| 2. C53×C9⋊H(3,𝔽3) | C3 | semidirect |
| 3. C9×H(3,𝔽3)×C53 | C3 | semidirect |
| 4. C53×#6861 | C3 | semidirect |
| 5. C53×#6861 | C3 | semidirect |
| 6. C53×#6859 | C3 | semidirect |
| 7. C53×#6859 | C3 | semidirect |
| 8. C53×#6856 | C3 | semidirect |
| 9. C53×#6856 | C3 | semidirect |
| 42. #10624654 | C53 | direct (N × H) |
| 62. #6895 | C3×C53 | semidirect |
| 63. C9⋊H(3,𝔽3) | C3×C53 | semidirect |
| 64. C9×H(3,𝔽3) | C3×C53 | semidirect |
| 65. #6861 | C3×C53 | semidirect |
| 66. #6861 | C3×C53 | semidirect |
| 67. #6859 | C3×C53 | semidirect |
| 68. #6859 | C3×C53 | semidirect |
| 69. #6856 | C3×C53 | semidirect |
| 70. #6856 | C3×C53 | semidirect |
| 93. C53 | #10624654 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#6895 | 3 |
| C53×C9⋊H(3,𝔽3) | 3 |
| C9×H(3,𝔽3)×C53 | 3 |
| C53×#6861 | 3 |
| C53×#6859 | 3 |
| C53×#6856 | 3 |
| #10624654 | 53 |