Finite Group DatabasebetaFinite Group DatabasebetaOrder 3645.
476 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 104 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 | C32×C5×H(3,𝔽3) | C3 |
| LCS | G ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C5 ◁ C34×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#6891 | C3 | semidirect |
| 3. C3×C5×C32⋊C9 | C3 | semidirect |
| 4. C5×H(3,𝔽3)⋊C9 | C3 | semidirect |
| 5. #10624777 | C5 | direct (N × H) |
| 12. C32×C5×C9 | C32 | semidirect |
| 16. C5×C32⋊C9 | C32 | semidirect |
| 18. #6891 | C3×C5 | semidirect |
| 19. C3×C32⋊C9 | C3×C5 | semidirect |
| 20. H(3,𝔽3)⋊C9 | C3×C5 | semidirect |
| 36. C5×H(3,𝔽3) | 3−1+2 | semidirect |
| 46. C32×C9 | C32×C5 | semidirect |
| 50. C32⋊C9 | C32×C5 | semidirect |
| 87. H(3,𝔽3) | C5×3−1+2 | semidirect |
| 120. C5 | #10624777 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×H(3,𝔽3) | 3 |
| C5×#6891 | 3 |
| C3×C5×C32⋊C9 | 3 |
| C5×H(3,𝔽3)⋊C9 | 3 |
| #10624777 | 5 |