Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
186 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 1. C2×C9×M16 | C2 | semidirect |
| 3. C2×C8×D9 | C2 | semidirect |
| 4. #63389 | C2 | semidirect |
| 5. (C2×D9)⋊C8 | C2 | semidirect |
| 6. #63375 | C2 | semidirect |
| 7. Dic9⋊C8 | C2 | semidirect |
| 42. C8×C9 | D4 | semidirect |
| 65. C2×D9 | M16 | semidirect |
| 72. C2×M16 | D9 | semidirect |
| 126. C9 | #435 | semidirect |
| 142. C8 | #611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×M16 | 2 |
| C4×#611 | 2 |
| C2×C8×D9 | 2 |
| #63389 | 2 |
| (C2×D9)⋊C8 | 2 |
| #63375 | 2 |
| Dic9⋊C8 | 2 |
| #5127 | 3 |