Finite Group DatabasebetaFinite Group DatabasebetaOrder 3600.
346 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #11925359 | C3 | direct (N × H) |
| 7. C3×C3⋊#1043 | C4 | semidirect |
| 8. C32×#1044 | C4 | semidirect |
| 9. C3×C5×Dic15 | C4 | semidirect |
| 29. C3⋊#1043 | C3×C4 | semidirect |
| 31. C3×#1044 | Dic3 | semidirect |
| 32. C3×#1044 | C3×C4 | semidirect |
| 34. C5×Dic15 | C3×C4 | semidirect |
| 38. C32×C52 | C42 | semidirect |
| 47. C3×Dic15 | AGL(1,𝔽5) | semidirect |
| 69. #1044 | C3×Dic3 | semidirect |
| 80. C3×C52 | C4×Dic3 | semidirect |
| 81. C3×C52 | C3×C42 | semidirect |
| 99. Dic15 | C3×AGL(1,𝔽5) | semidirect |
| 108. C32×C5 | C4×AGL(1,𝔽5) | semidirect |
| 135. C52 | C3×C4×Dic3 | semidirect |
| 158. C3×C5 | Dic3×AGL(1,𝔽5) | semidirect |
| 159. C3×C5 | C3×C4×AGL(1,𝔽5) | semidirect |
| 176. C32 | #87830 | semidirect |
| 190. C5 | C3×Dic3×AGL(1,𝔽5) | semidirect |
| 196. C3 | C3×#87830 | semidirect |
| 197. C3 | #11925359 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C3⋊#1043 | 2 |
| C2×C32×#1044 | 2 |
| C3×#10597126 | 2 |
| #11925359 | 3 |
| C3×#87830 | 3 |
| C3×Dic3×AGL(1,𝔽5) | 5 |