Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
201 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 201 conjugacy classes of subgroups — too many to draw. Only its 81 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. D4×Dic9 | C2 | semidirect |
| 3. #63392 | C2 | semidirect |
| 4. #63378 | C2 | semidirect |
| 5. C8×Dic9 | C2 | semidirect |
| 9. C9×D8 | C4 | semidirect |
| 22. D4×C9 | C2×C4 | semidirect |
| 28. C8×C9 | C2×C4 | semidirect |
| 47. Dic9 | D8 | direct (N × H) |
| 69. D8 | Dic9 | direct (N × H) |
| 84. C9 | C4×D8 | semidirect |
| 87. D4 | C2×Dic9 | semidirect |
| 94. C8 | C2×Dic9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D8 | 2 |
| D4×Dic9 | 2 |
| #63392 | 2 |
| #63378 | 2 |
| C8×Dic9 | 2 |
| Dic3×D8 | 3 |