Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
432 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×C32×D8 | C2 | semidirect |
| 2. #64149 | C2 | semidirect |
| 3. #64145 | C2 | semidirect |
| 4. C2×#3754 | C2 | semidirect |
| 5. C2×#3753 | C2 | semidirect |
| 6. C2×#3744 | C2 | semidirect |
| 7. #63642 | C2 | semidirect |
| 22. C2×C3×D8 | D3 | semidirect |
| 44. C32×C8 | D4 | semidirect |
| 45. C3⋊(C3⋊C8) | D4 | semidirect |
| 74. C2×D8 | C3⋊D3 | semidirect |
| 93. C3×C8 | #67 | semidirect |
| 124. C32 | #496 | semidirect |
| 141. C8 | #638 | semidirect |
| 158. C3 | #5154 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D8 | 2 |
| #64149 | 2 |
| #64145 | 2 |
| C2×#3754 | 2 |
| C2×#3753 | 2 |
| C2×#3744 | 2 |
| #63642 | 2 |
| #5154 | 3 |