Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
758 conjugacy classes of subgroups; only the 494 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 494 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, Frattini, cosocle | C32 | C34×C37 |
| socle | C32×C37 | C34 |
| prime radical | C3×H(3,𝔽3)×C37 | C32 |
| 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 |
|---|---|---|
| 2. C37×#6900 | C3 | semidirect |
| 3. C37×#6899 | C3 | semidirect |
| 4. C37×#6896 | C3 | semidirect |
| 5. C37×#6894 | C3 | semidirect |
| 7. C9×3−1+2×C37 | C3 | semidirect |
| 8. C37×#6887 | C3 | semidirect |
| 9. C3×C92×C37 | C3 | semidirect |
| 39. C3×C9×C37 | 3−1+2 | semidirect |
| 47. #10624879 | C37 | direct (N × H) |
| 59. C9×C37 | #737 | semidirect |
| 61. #6900 | C3×C37 | semidirect |
| 62. #6899 | C3×C37 | semidirect |
| 63. #6896 | C3×C37 | semidirect |
| 64. #6894 | C3×C37 | semidirect |
| 66. C9×3−1+2 | C3×C37 | semidirect |
| 67. #6887 | C3×C37 | semidirect |
| 68. C3×C92 | C3×C37 | semidirect |
| 93. C37 | #10624879 | direct (N × H) |
| 103. C3×C9 | 3−1+2×C37 | semidirect |
| 122. C9 | C37×#737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C37×#737 | 3 |
| C37×#6900 | 3 |
| C37×#6899 | 3 |
| C37×#6896 | 3 |
| C37×#6894 | 3 |
| C37×C9⋊H(3,𝔽3) | 3 |
| C9×3−1+2×C37 | 3 |
| C37×#6887 | 3 |
| C3×C92×C37 | 3 |
| #10624879 | 37 |