Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
372 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 107 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. C32×C4×D4 | C2 | semidirect |
| 2. C2×#3754 | C2 | semidirect |
| 4. #64084 | C2 | semidirect |
| 5. #63637 | C2 | semidirect |
| 6. #63636 | C2 | semidirect |
| 7. C4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 22. C3×C4×D4 | D3 | semidirect |
| 75. C4×D4 | C3⋊D3 | semidirect |
| 126. C32 | #463 | semidirect |
| 161. C3 | #5016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×D4 | 2 |
| C2×#3754 | 2 |
| C2×#3753 | 2 |
| #64084 | 2 |
| #63637 | 2 |
| #63636 | 2 |
| C4⋊(C3⋊(C3⋊C8)) | 2 |
| #5016 | 3 |