Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
558 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 151 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×C32×M16 | C2 | semidirect |
| 3. C2×#3748 | C2 | semidirect |
| 4. #63650 | C2 | direct (N × H) |
| 15. C32×M16 | C22 | semidirect |
| 18. #3748 | C22 | semidirect |
| 21. C2×C3×M16 | D3 | semidirect |
| 51. C3×M16 | C2×D3 | semidirect |
| 70. C2×M16 | C3⋊D3 | semidirect |
| 91. C2×C32 | #100 | semidirect |
| 105. M16 | C2×C3⋊D3 | semidirect |
| 120. C32 | C2×#100 | semidirect |
| 140. C2×C3 | #823 | semidirect |
| 155. C3 | C2×#823 | semidirect |
| 159. C2 | #63650 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C3⋊D3) | 2 |
| C2×C32×M16 | 2 |
| C2×#3748 | 2 |
| #63650 | 2 |
| C2×#823 | 3 |