Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
405 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 405 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 |
|---|---|---|
| 2. C2×C3×ΓL(1,𝔽25) | C2 | semidirect |
| 3. C32×C22⋊C8 | C2 | semidirect |
| 4. C3×#830 | C2 | semidirect |
| 5. C3×(C2×D3)⋊C8 | C2 | semidirect |
| 7. #4726 | C3 | direct (N × H) |
| 16. C2×C32×C8 | C22 | semidirect |
| 17. C2×C3×C3⋊C8 | C22 | semidirect |
| 22. C2×ΓL(1,𝔽25) | C2×C3 | semidirect |
| 26. C3×C22⋊C8 | D3 | semidirect |
| 27. C3×C22⋊C8 | C2×C3 | semidirect |
| 28. #830 | C2×C3 | semidirect |
| 29. (C2×D3)⋊C8 | C2×C3 | semidirect |
| 69. C2×C3×C8 | C2×D3 | semidirect |
| 70. C2×C3×C8 | C22×C3 | semidirect |
| 71. C2×C3⋊C8 | C22×C3 | semidirect |
| 75. C22×C32 | M16 | semidirect |
| 83. C2×C3×D3 | M16 | semidirect |
| 92. C22⋊C8 | C3×D3 | semidirect |
| 150. C2×C8 | C2×C3×D3 | semidirect |
| 166. C22×C3 | ΓL(1,𝔽25) | semidirect |
| 167. C22×C3 | C3×M16 | semidirect |
| 176. C2×D3 | C3×M16 | semidirect |
| 187. C32 | #407 | semidirect |
| 231. C22 | C3×ΓL(1,𝔽25) | semidirect |
| 238. C3 | #4726 | direct (N × H) |
| 239. C3 | C3×#407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×D3 | 2 |
| C2×C3×ΓL(1,𝔽25) | 2 |
| C32×C22⋊C8 | 2 |
| C3×#830 | 2 |
| C3×(C2×D3)⋊C8 | 2 |
| C3×#407 | 3 |
| #4726 | 3 |