Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
192 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C3×C9×C37 | C33 |
| commutator | C32 | C32×C9×C37 |
| Frattini, cosocle | C3×C9 | C33×C37 |
| socle | C32×C37 | C32×C9 |
| prime radical | C33×C37 | C3×C9 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C3×C9×C37 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C37×C9⋊C27 | C3 | semidirect |
| 4. C37×C9⋊C27 | C3 | semidirect |
| 6. C37×#6864 | C3 | semidirect |
| 7. C9×C27×C37 | C3 | semidirect |
| 33. C27×C37 | 3−1+2 | semidirect |
| 34. #10624728 | C37 | direct (N × H) |
| 43. C9×C37 | C27⋊C3 | semidirect |
| 48. C9⋊C27 | C3×C37 | semidirect |
| 49. C9⋊C27 | C3×C37 | semidirect |
| 51. #6864 | C3×C37 | semidirect |
| 52. C9×C27 | C3×C37 | semidirect |
| 69. C37 | #10624728 | direct (N × H) |
| 83. C27 | 3−1+2×C37 | semidirect |
| 92. C9 | C37×C27⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C37×C27⋊C3 | 3 |
| C9×3−1+2×C37 | 3 |
| C37×C9⋊C27 | 3 |
| C37×C32⋊C27 | 3 |
| C37×#6864 | 3 |
| C9×C27×C37 | 3 |
| #10624728 | 37 |