Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
345 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 345 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×#103 | C2 | semidirect |
| 5. C3×#835 | C2 | semidirect |
| 6. C3×#821 | C2 | semidirect |
| 7. C3×#809 | C2 | semidirect |
| 9. #4803 | C3 | direct (N × H) |
| 12. C3×#239 | C4 | semidirect |
| 28. C2×ΓL(1,𝔽25) | C2×C3 | semidirect |
| 29. D3×C4⋊C4 | C2×C3 | semidirect |
| 32. C3×#103 | D3 | semidirect |
| 33. C3×#103 | C2×C3 | semidirect |
| 36. #835 | C2×C3 | semidirect |
| 37. #821 | C2×C3 | semidirect |
| 38. #809 | C2×C3 | semidirect |
| 42. C32×Q8 | C2×C4 | semidirect |
| 50. C3×D12 | C2×C4 | semidirect |
| 69. #239 | C3×C4 | semidirect |
| 106. #103 | C3×D3 | semidirect |
| 117. C3×Q8 | C4×D3 | semidirect |
| 118. C3×Q8 | C2×C3×C4 | semidirect |
| 141. D12 | C2×C3×C4 | semidirect |
| 201. C32 | #417 | semidirect |
| 205. Q8 | C3×C4×D3 | semidirect |
| 247. C3 | #4803 | direct (N × H) |
| 248. 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×#239 | 2 |
| C2×C3×ΓL(1,𝔽25) | 2 |
| C3×D3×C4⋊C4 | 2 |
| C32×#103 | 2 |
| C3×#835 | 2 |
| C3×#821 | 2 |
| C3×#809 | 2 |
| C3×#417 | 3 |
| #4803 | 3 |