Finite Group DatabasebetaFinite Group DatabasebetaOrder 3645.
312 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C5×C9 | C3×H(3,𝔽3) |
| commutator | C32 | C32×C5×C9 |
| Frattini, cosocle | C3×C9 | C33×C5 |
| socle | C3×C5 | C3×C32⋊C9 |
| prime radical | C3×C5×H(3,𝔽3) | C9 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C5×C9 ◁ C32×C5×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C5×C27⋊C3 | C3 | semidirect |
| 3. C3×C5×C27⋊C3 | C3 | semidirect |
| 4. C5×#6873 | C3 | semidirect |
| 5. #10624704 | C5 | direct (N × H) |
| 19. C5×C27⋊C3 | C32 | semidirect |
| 21. C3×C5×C27 | C32 | semidirect |
| 23. C3×C27⋊C3 | C3×C5 | semidirect |
| 24. C3×C27⋊C3 | C3×C5 | semidirect |
| 25. #6873 | C3×C5 | semidirect |
| 58. C27⋊C3 | C32×C5 | semidirect |
| 60. C3×C27 | C32×C5 | semidirect |
| 107. C5 | #10624704 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#737 | 3 |
| C3×C5×C27⋊C3 | 3 |
| C5×#6873 | 3 |
| #10624704 | 5 |