Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
237 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 237 conjugacy classes of subgroups — too many to draw. Only its 85 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×C9×M16 | C2 | semidirect |
| 3. C22×C9⋊C8 | C2 | semidirect |
| 4. (C2×D9)⋊C8 | C2 | semidirect |
| 57. C2×M16 | D9 | semidirect |
| 98. C9 | #408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3697 | 2 |
| C2×C9×M16 | 2 |
| C22×C9⋊C8 | 2 |
| (C2×D9)⋊C8 | 2 |
| #5129 | 3 |