Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
788 conjugacy classes of subgroups; only the 446 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 446 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×C37 | C34 |
| commutator, Frattini, cosocle | C32 | C34×C37 |
| prime radical | C37×C32⋊H(3,𝔽3) | C3 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C37 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C37×#6893 | C3 | semidirect |
| 2. C37×C9⋊H(3,𝔽3) | C3 | semidirect |
| 3. C37×C9⋊H(3,𝔽3) | C3 | semidirect |
| 4. C37×#6891 | C3 | semidirect |
| 6. C9×H(3,𝔽3)×C37 | C3 | semidirect |
| 7. C3×C37×C32⋊C9 | C3 | semidirect |
| 10. C3×3−1+2×C37 | C32 | semidirect |
| 15. C32×C9×C37 | C32 | semidirect |
| 22. C37×C32⋊C9 | C32 | semidirect |
| 23. C37×C32⋊C9 | C32 | semidirect |
| 41. #10624905 | C37 | direct (N × H) |
| 60. #6893 | C3×C37 | semidirect |
| 61. C9⋊H(3,𝔽3) | C3×C37 | semidirect |
| 62. C9⋊H(3,𝔽3) | C3×C37 | semidirect |
| 63. #6891 | C3×C37 | semidirect |
| 65. C9×H(3,𝔽3) | C3×C37 | semidirect |
| 66. C3×C32⋊C9 | C3×C37 | semidirect |
| 76. C3×3−1+2 | C32×C37 | semidirect |
| 81. C32×C9 | C32×C37 | semidirect |
| 88. C32⋊C9 | C32×C37 | semidirect |
| 89. C32⋊C9 | C32×C37 | semidirect |
| 90. C37 | #10624905 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C37×#6893 | 3 |
| C37×C9⋊H(3,𝔽3) | 3 |
| C37×#6891 | 3 |
| C37×C32⋊H(3,𝔽3) | 3 |
| C9×H(3,𝔽3)×C37 | 3 |
| C3×C37×C32⋊C9 | 3 |
| #10624905 | 37 |