Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 89 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. #64153 | C2 | semidirect |
| 5. C32×#103 | C2 | semidirect |
| 6. #63641 | C2 | semidirect |
| 7. #63637 | C2 | semidirect |
| 26. C3×#103 | D3 | semidirect |
| 69. C3⋊Dic3 | SD16 | semidirect |
| 76. #103 | C3⋊D3 | semidirect |
| 121. C32 | #461 | semidirect |
| 153. C3 | #4818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64153 | 2 |
| C2×#3755 | 2 |
| C2×#3744 | 2 |
| #64102 | 2 |
| C32×#103 | 2 |
| #63641 | 2 |
| #63637 | 2 |
| #4818 | 3 |