Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
222 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 92 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 | C33×C37 | C33 |
| 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 |
|---|---|---|
| 39. #10624799 | C37 | direct (N × H) |
| 52. C9×C37 | #733 | semidirect |
| 79. C37 | #10624799 | direct (N × H) |
| 109. C9 | C37×#733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C37×#733 | 3 |
| C37×#6894 | 3 |
| C9×3−1+2×C37 | 3 |
| C3×C37×C9⋊C9 | 3 |
| C37×3−1+2⋊C9 | 3 |
| C37×#6868 | 3 |
| #10624799 | 37 |