Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
243 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 243 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. C2×C4⋊Dic9 | C2 | semidirect |
| 4. #63380 | C2 | semidirect |
| 5. #63376 | C2 | semidirect |
| 11. #3697 | C4 | semidirect |
| 35. D36 | C2×C4 | semidirect |
| 38. Dic18 | C2×C4 | semidirect |
| 66. C2×M16 | D9 | semidirect |
| 115. C9 | #417 | 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 |
| C2×C4⋊Dic9 | 2 |
| #63380 | 2 |
| #63376 | 2 |
| #5133 | 3 |