Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
620 conjugacy classes of subgroups; only the 440 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 440 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 | C34×C37 | C32 |
| 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×#6897 | C3 | semidirect |
| 2. C37×#6896 | C3 | semidirect |
| 3. C37×#6894 | C3 | semidirect |
| 6. C9×3−1+2×C37 | C3 | semidirect |
| 13. C37×C9⋊C9 | C32 | semidirect |
| 14. C37×C9⋊C9 | C32 | semidirect |
| 21. C92×C37 | C32 | semidirect |
| 36. #10624889 | C37 | direct (N × H) |
| 52. #6897 | C3×C37 | semidirect |
| 53. #6896 | C3×C37 | semidirect |
| 54. #6894 | C3×C37 | semidirect |
| 57. C9×3−1+2 | C3×C37 | semidirect |
| 70. C9⋊C9 | C32×C37 | semidirect |
| 71. C9⋊C9 | C32×C37 | semidirect |
| 78. C92 | C32×C37 | semidirect |
| 79. C37 | #10624889 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C37×#6897 | 3 |
| C37×#6896 | 3 |
| C37×#6894 | 3 |
| C37×#6891 | 3 |
| C9×3−1+2×C37 | 3 |
| C3×C37×C32⋊C9 | 3 |
| #10624889 | 37 |