Finite Group DatabasebetaFinite Group DatabasebetaOrder 38637.
178 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C53 | #6911 |
| commutator, Frattini, cosocle | C3×C9 | C33×C53 |
| LCS | G ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C53 ◁ C32×C53 ◁ C3×3−1+2×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C53×#6913 | C3 | semidirect |
| 2. C53×#6912 | C3 | semidirect |
| 3. C53×#6899 | C3 | semidirect |
| 4. C53×#6883 | C3 | semidirect |
| 5. C53×#6882 | C3 | semidirect |
| 6. C53×#6882 | C3 | semidirect |
| 7. C53×#6881 | C3 | semidirect |
| 8. C53×#6880 | C3 | semidirect |
| 9. C53×#6878 | C3 | semidirect |
| 42. #10624854 | C53 | direct (N × H) |
| 56. #6913 | C3×C53 | semidirect |
| 57. #6912 | C3×C53 | semidirect |
| 58. #6899 | C3×C53 | semidirect |
| 59. #6883 | C3×C53 | semidirect |
| 60. #6882 | C3×C53 | semidirect |
| 61. #6882 | C3×C53 | semidirect |
| 62. #6881 | C3×C53 | semidirect |
| 63. #6880 | C3×C53 | semidirect |
| 64. #6878 | C3×C53 | semidirect |
| 85. C53 | #10624854 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#6913 | 3 |
| C53×#6912 | 3 |
| C53×#6899 | 3 |
| C53×#6883 | 3 |
| C53×#6882 | 3 |
| C53×#6881 | 3 |
| C53×#6880 | 3 |
| C53×#6878 | 3 |
| #10624854 | 53 |