Finite Group DatabasebetaFinite Group DatabasebetaOrder 3600.
314 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 70 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. #11925351 | C3 | direct (N × H) |
| 9. C32×C5×Dic5 | C4 | semidirect |
| 34. C3×C5×Dic5 | Dic3 | semidirect |
| 35. C3×C5×Dic5 | C3×C4 | semidirect |
| 38. C32×C52 | C4⋊C4 | semidirect |
| 49. C32×Dic5 | AGL(1,𝔽5) | semidirect |
| 72. C5×Dic5 | C3×Dic3 | semidirect |
| 81. C3×C52 | C4⋊Dic3 | semidirect |
| 82. C3×C52 | C3×C4⋊C4 | semidirect |
| 104. C3×Dic5 | C3×AGL(1,𝔽5) | semidirect |
| 105. C3×Dic5 | ΓL(1,𝔽16) | semidirect |
| 112. C32×C5 | C4⋊AGL(1,𝔽5) | semidirect |
| 139. C52 | C3×C4⋊Dic3 | semidirect |
| 154. Dic5 | C3×ΓL(1,𝔽16) | semidirect |
| 163. C3×C5 | C3×C4⋊AGL(1,𝔽5) | semidirect |
| 164. C3×C5 | C4⋊ΓL(1,𝔽16) | semidirect |
| 181. C32 | #87832 | semidirect |
| 195. C5 | C3×C4⋊ΓL(1,𝔽16) | semidirect |
| 201. C3 | C3×#87832 | semidirect |
| 202. C3 | #11925351 | 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⋊#1044 | 2 |
| C2×C3×C3⋊#1043 | 2 |
| C32×#6036 | 2 |
| #11925351 | 3 |
| C3×#87832 | 3 |
| C3×C4⋊ΓL(1,𝔽16) | 5 |