Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
372 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 97 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×#124 | C2 | semidirect |
| 2. C2×#3755 | C2 | semidirect |
| 4. C4×C4⋊(C3⋊D3) | C2 | semidirect |
| 5. #63662 | C2 | semidirect |
| 6. #63659 | C2 | semidirect |
| 7. C4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 22. C3×#124 | D3 | semidirect |
| 74. #124 | C3⋊D3 | semidirect |
| 126. C32 | #463 | semidirect |
| 161. C3 | #5057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#124 | 2 |
| C2×#3755 | 2 |
| C2×#3753 | 2 |
| C4×C4⋊(C3⋊D3) | 2 |
| #63662 | 2 |
| #63659 | 2 |
| C4⋊(C3⋊(C3⋊C8)) | 2 |
| #5057 | 3 |