Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
413 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 413 conjugacy classes of subgroups — too many to draw. Only its 80 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. #64133 | C2 | semidirect |
| 3. C2×#3716 | C2 | semidirect |
| 4. C3×#830 | C2 | semidirect |
| 5. #63563 | C2 | semidirect |
| 10. C2×#634 | C22 | semidirect |
| 15. C4⋊(C3⋊Dic3) | C22 | semidirect |
| 17. C2×C3×C3⋊C8 | C22 | semidirect |
| 28. #830 | D3 | semidirect |
| 71. C2×C3⋊C8 | C2×D3 | semidirect |
| 75. C22×C32 | SD16 | semidirect |
| 155. C22×C3 | #204 | semidirect |
| 156. C22×C3 | #214 | semidirect |
| 175. C32 | #450 | semidirect |
| 211. C22 | #3716 | semidirect |
| 218. C3 | #4731 | semidirect |
| 219. C3 | #5218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D12 | 2 |
| #64133 | 2 |
| C2×#3716 | 2 |
| C3×#830 | 2 |
| #63563 | 2 |
| #5218 | 3 |
| #4731 | 3 |