Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
238 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 80 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 | C3×H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C33×C37 |
| prime radical | C34×C37 | C32 |
| LCS | G ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C37 ◁ C32×C9×C37 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C37×#6895 | C3 | semidirect |
| 2. C37×#6887 | C3 | semidirect |
| 4. C37×#6868 | C3 | semidirect |
| 5. C37×#6868 | C3 | semidirect |
| 6. C37×#6867 | C3 | semidirect |
| 7. C37×#6867 | C3 | semidirect |
| 42. #10624810 | C37 | direct (N × H) |
| 60. #6895 | C3×C37 | semidirect |
| 61. #6887 | C3×C37 | semidirect |
| 63. #6868 | C3×C37 | semidirect |
| 64. #6868 | C3×C37 | semidirect |
| 65. #6867 | C3×C37 | semidirect |
| 66. #6867 | C3×C37 | semidirect |
| 89. C37 | #10624810 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C37×#6895 | 3 |
| C37×#6887 | 3 |
| C3×C37×C32⋊C9 | 3 |
| C37×#6868 | 3 |
| C37×#6867 | 3 |
| C37×#6866 | 3 |
| #10624810 | 37 |