Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
306 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 1. C2×#3753 | C2 | semidirect |
| 2. C3×#938 | C2 | semidirect |
| 3. #63909 | C2 | semidirect |
| 4. C2×D3×C3⋊C8 | C2 | semidirect |
| 5. C3×#832 | C2 | semidirect |
| 6. #63576 | C2 | semidirect |
| 7. #63564 | C2 | semidirect |
| 24. #938 | D3 | semidirect |
| 33. #832 | D3 | semidirect |
| 53. C3⋊(C3⋊C8) | D4 | semidirect |
| 95. C2×C3×D3 | D8 | semidirect |
| 195. C2×D3 | #213 | semidirect |
| 208. C32 | #466 | semidirect |
| 259. C3 | #4775 | semidirect |
| 260. C3 | #5038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3753 | 2 |
| C3×#938 | 2 |
| #63909 | 2 |
| C2×D3×C3⋊C8 | 2 |
| C3×#832 | 2 |
| #63576 | 2 |
| #63564 | 2 |
| #5038 | 3 |
| #4775 | 3 |