Finite Group DatabasebetaFinite Group DatabasebetaOrder 3600.
104 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 28 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 |
|---|---|---|
| 2. C3×AGL(1,𝔽25) | C2 | semidirect |
| 3. C3×#10597167 | C2 | semidirect |
| 5. AΓL(1,𝔽25) | C3 | direct (N × H) |
| 11. C3×#6053 | D3 | semidirect |
| 14. AGL(1,𝔽25) | C2×C3 | semidirect |
| 15. #10597167 | C2×C3 | semidirect |
| 26. C3×C52⋊C3 | M16 | semidirect |
| 29. #6053 | C3×D3 | semidirect |
| 40. C3×C52 | ΓL(1,𝔽25) | semidirect |
| 42. C52⋊C3 | C3×M16 | semidirect |
| 60. C52 | C3×ΓL(1,𝔽25) | semidirect |
| 100. C3 | AΓL(1,𝔽25) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64480⋊C2 | 2 |
| C3×AGL(1,𝔽25) | 2 |
| C3×#10597167 | 2 |
| C3×#6053⋊C2 | 3 |
| AΓL(1,𝔽25) | 3 |
| C3×ΓL(1,𝔽25) | 25 |