Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
349 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 349 conjugacy classes of subgroups — too many to draw. Only its 110 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. C3×D3×C4⋊C4 | C2 | semidirect |
| 4. C32×#102 | C2 | semidirect |
| 5. C3×#832 | C2 | semidirect |
| 6. C3×#816 | C2 | semidirect |
| 7. C3×#810 | C2 | semidirect |
| 9. #4771 | C3 | direct (N × H) |
| 14. C3×#237 | C4 | semidirect |
| 28. C2×ΓL(1,𝔽25) | C2×C3 | semidirect |
| 29. D3×C4⋊C4 | C2×C3 | semidirect |
| 34. C3×#102 | D3 | semidirect |
| 35. C3×#102 | C2×C3 | semidirect |
| 36. #832 | C2×C3 | semidirect |
| 37. #816 | C2×C3 | semidirect |
| 38. #810 | C2×C3 | semidirect |
| 42. C32×D4 | C2×C4 | semidirect |
| 54. C3×Dic6 | C2×C4 | semidirect |
| 71. #237 | C3×C4 | semidirect |
| 108. #102 | C3×D3 | semidirect |
| 121. C3×D4 | C4×D3 | semidirect |
| 122. C3×D4 | C2×C3×C4 | semidirect |
| 145. Dic6 | C2×C3×C4 | semidirect |
| 203. C32 | #417 | semidirect |
| 210. D4 | C3×C4×D3 | semidirect |
| 250. C3 | #4771 | direct (N × H) |
| 251. C3 | C3×#417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#237 | 2 |
| C2×C3×ΓL(1,𝔽25) | 2 |
| C3×D3×C4⋊C4 | 2 |
| C32×#102 | 2 |
| C3×#832 | 2 |
| C3×#816 | 2 |
| C3×#810 | 2 |
| C3×#417 | 3 |
| #4771 | 3 |