Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
254 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C33 | C32×C37⋊C3 |
| commutator, socle, prime radical, cosocle | C33×C37 | C33 |
| Fitting | C37×#6855 | C3 |
| hypercenter | #6855 | C37⋊C3 |
| hypocenter | C37 | #10624576 |
| LCS | G ▷ C33×C37 ▷ C37 | |
| UCS | C1 ◁ C33 ◁ #6855 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 148. C37 | #10624576 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688504 | 3 |
| #22582441 | 3 |
| C37×#6855 | 3 |
| #10624576 | 37 |