Finite Group DatabasebetaFinite Group DatabasebetaOrder 3645.
356 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 86 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×C5 | C3×H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C33×C5 |
| prime radical | C34×C5 | C32 |
| LCS | G ▷ C33 ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C5 ◁ C34×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C5×#6858 | C3 | semidirect |
| 6. #10624592 | C5 | direct (N × H) |
| 29. #6858 | C3×C5 | semidirect |
| 138. C5 | #10624592 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×3−1+2 | 3 |
| C5×#6891 | 3 |
| C3×C5×C32⋊C9 | 3 |
| C5×#6858 | 3 |
| #10624592 | 5 |