Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
932 conjugacy classes of subgroups; only the 548 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 548 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C33×C37 | C33 |
| commutator, Frattini, cosocle | C32 | C34×C37 |
| prime radical | C34×C37 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C33×C37 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C37×#6894 | C3 | direct (N × H) |
| 4. C3×C37×C9⋊C9 | C3 | semidirect |
| 5. C3×C37×C9⋊C9 | C3 | semidirect |
| 16. C37×C9⋊C9 | C32 | semidirect |
| 17. C37×C9⋊C9 | C32 | semidirect |
| 29. C3×C9×C37 | 3−1+2 | semidirect |
| 34. C3×#6894 | C37 | direct (N × H) |
| 46. C9×C37 | C3×3−1+2 | semidirect |
| 49. #6894 | C3×C37 | direct (N × H) |
| 50. C3×C9⋊C9 | C3×C37 | semidirect |
| 51. C3×C9⋊C9 | C3×C37 | semidirect |
| 54. C3×C37 | #6894 | direct (N × H) |
| 67. C9⋊C9 | C32×C37 | semidirect |
| 68. C9⋊C9 | C32×C37 | semidirect |
| 70. C37 | C3×#6894 | direct (N × H) |
| 81. C3×C9 | 3−1+2×C37 | semidirect |
| 97. C9 | C3×3−1+2×C37 | semidirect |
| 99. C3 | C37×#6894 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×3−1+2×C37 | 3 |
| C33×C9×C37 | 3 |
| C37×#6894 | 3 |
| C3×C37×C9⋊C9 | 3 |
| C3×C37×C32⋊C9 | 3 |
| C3×#6894 | 37 |