Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
271 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 271 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 3. C32×C4⋊C8 | C2 | semidirect |
| 4. C3×Dic3⋊C8 | C2 | semidirect |
| 5. C3×C4⋊(C3⋊C8) | C2 | semidirect |
| 7. #4837 | C3 | direct (N × H) |
| 25. C3×C4⋊C8 | D3 | semidirect |
| 26. C3×C4⋊C8 | C2×C3 | semidirect |
| 27. Dic3⋊C8 | C2×C3 | semidirect |
| 28. C4⋊(C3⋊C8) | C2×C3 | semidirect |
| 70. C32×C4 | M16 | semidirect |
| 75. C3×Dic3 | M16 | semidirect |
| 80. C4⋊C8 | C3×D3 | semidirect |
| 143. C3×C4 | ΓL(1,𝔽25) | semidirect |
| 144. C3×C4 | C3×M16 | semidirect |
| 151. Dic3 | C3×M16 | semidirect |
| 152. C32 | #423 | semidirect |
| 185. C4 | C3×ΓL(1,𝔽25) | semidirect |
| 189. C3 | #4837 | direct (N × H) |
| 190. C3 | C3×#423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×ΓL(1,𝔽25) | 2 |
| C3×C42×D3 | 2 |
| C32×C4⋊C8 | 2 |
| C3×Dic3⋊C8 | 2 |
| C3×C4⋊(C3⋊C8) | 2 |
| C3×#423 | 3 |
| #4837 | 3 |