Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
324 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 75 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. #64141 | C2 | semidirect |
| 2. C2×#3753 | C2 | semidirect |
| 3. #64117 | C2 | semidirect |
| 4. #64116 | C2 | semidirect |
| 5. C32×#100 | C2 | semidirect |
| 6. #63650 | C2 | semidirect |
| 7. #63649 | C2 | semidirect |
| 28. C3×#100 | D3 | semidirect |
| 78. #100 | C3⋊D3 | semidirect |
| 124. C32 | #472 | semidirect |
| 155. C3 | #4749 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64141 | 2 |
| C2×#3753 | 2 |
| #64117 | 2 |
| #64116 | 2 |
| C32×#100 | 2 |
| #63650 | 2 |
| #63649 | 2 |
| #4749 | 3 |