Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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. C2×#3754 | C2 | semidirect |
| 3. C2×#3743 | C2 | semidirect |
| 4. #64106 | C2 | semidirect |
| 5. C32×#102 | C2 | semidirect |
| 6. #63643 | C2 | semidirect |
| 7. #63634 | C2 | semidirect |
| 26. C3×#102 | D3 | semidirect |
| 44. C3⋊(C3⋊C8) | D4 | semidirect |
| 78. #102 | C3⋊D3 | semidirect |
| 126. C32 | #468 | semidirect |
| 161. C3 | #4780 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64147 | 2 |
| C2×#3754 | 2 |
| C2×#3743 | 2 |
| #64106 | 2 |
| C32×#102 | 2 |
| #63643 | 2 |
| #63634 | 2 |
| #4780 | 3 |