Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
253 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 253 conjugacy classes of subgroups — too many to draw. Only its 86 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×C4⋊Dic3 | C2 | semidirect |
| 3. C32×C22⋊C8 | C2 | semidirect |
| 4. C3×#821 | C2 | semidirect |
| 5. C3×#817 | C2 | semidirect |
| 7. #4735 | C3 | direct (N × H) |
| 20. C2×C4⋊Dic3 | C2×C3 | semidirect |
| 24. C3×C22⋊C8 | D3 | semidirect |
| 25. C3×C22⋊C8 | C2×C3 | semidirect |
| 26. #821 | C2×C3 | semidirect |
| 27. #817 | C2×C3 | semidirect |
| 75. C22⋊C8 | C3×D3 | semidirect |
| 145. C32 | #481 | semidirect |
| 183. C3 | #4735 | direct (N × H) |
| 184. C3 | C3×#481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#930 | 2 |
| C2×C3×C4⋊Dic3 | 2 |
| C32×C22⋊C8 | 2 |
| C3×#821 | 2 |
| C3×#817 | 2 |
| C3×#481 | 3 |
| #4735 | 3 |