Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
312 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 85 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. #64118 | C2 | semidirect |
| 3. C2×#3744 | C2 | semidirect |
| 4. #64110 | C2 | semidirect |
| 5. C32×#108 | C2 | semidirect |
| 6. #63651 | C2 | semidirect |
| 7. #63650 | C2 | semidirect |
| 28. C3×#108 | D3 | semidirect |
| 75. #108 | C3⋊D3 | semidirect |
| 121. C32 | #471 | semidirect |
| 150. C3 | #4898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64118 | 2 |
| #64117 | 2 |
| C2×#3744 | 2 |
| #64110 | 2 |
| C32×#108 | 2 |
| #63651 | 2 |
| #63650 | 2 |
| #4898 | 3 |