Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
374 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 206 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C33×C37 | C33 |
| commutator | C32 | C32×C9×C37 |
| Frattini, cosocle | C33 | C33×C37 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C33×C37 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 16. C37×C9⋊C9 | C9 | semidirect |
| 36. #10624561 | C37 | direct (N × H) |
| 48. C9×C37 | C9⋊C9 | semidirect |
| 70. C9⋊C9 | C9×C37 | semidirect |
| 72. C37 | #10624561 | direct (N × H) |
| 102. C9 | C37×C9⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C37×C9⋊C9 | 3 |
| C3×C92×C37 | 3 |
| C37×#6855 | 3 |
| #10624561 | 37 |