Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
180 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 55 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×#3672 | C2 | semidirect |
| 3. #63486 | C2 | semidirect |
| 4. C2×#3667 | C2 | semidirect |
| 5. #63392 | C2 | semidirect |
| 6. #63368 | C2 | semidirect |
| 7. #63366 | C2 | semidirect |
| 44. C9⋊C8 | D4 | semidirect |
| 126. C9 | #468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#121 | 2 |
| C2×#3672 | 2 |
| #63486 | 2 |
| C2×#3667 | 2 |
| #63392 | 2 |
| #63368 | 2 |
| #63366 | 2 |
| #5042 | 3 |