Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
447 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 447 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×Dic18 | C2 | semidirect |
| 3. C22×C8×C9 | C2 | semidirect |
| 4. C2×#3664 | C2 | direct (N × H) |
| 12. C2×Dic18 | C22 | semidirect |
| 13. C2×C8×C9 | C22 | semidirect |
| 14. #3664 | C22 | direct (N × H) |
| 28. Dic18 | C23 | semidirect |
| 29. C8×C9 | C23 | semidirect |
| 40. C22×C9 | SD16 | semidirect |
| 50. C22×C8 | D9 | semidirect |
| 62. C2×C9 | C2×SD16 | semidirect |
| 73. C2×C8 | C2×D9 | semidirect |
| 81. C9 | C22×SD16 | semidirect |
| 92. C8 | C22×D9 | semidirect |
| 98. C22 | #3664 | direct (N × H) |
| 105. C2 | C2×#3664 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D36 | 2 |
| C22×Dic18 | 2 |
| C22×C8×C9 | 2 |
| C2×#3664 | 2 |
| C22×#204 | 3 |