Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
282 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 59 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×SD16 | C2 | semidirect |
| 3. #63508 | C2 | semidirect |
| 4. C2×#3675 | C2 | semidirect |
| 5. #63392 | C2 | semidirect |
| 6. #63380 | C2 | semidirect |
| 7. (C2×D9)⋊C8 | C2 | semidirect |
| 10. C2×Q8×C9 | C22 | semidirect |
| 18. C2×C8×C9 | C22 | semidirect |
| 21. C4⋊Dic9 | C22 | semidirect |
| 23. C2×C9⋊C8 | C22 | semidirect |
| 78. C2×D9 | SD16 | semidirect |
| 86. C2×SD16 | D9 | semidirect |
| 119. C2×Q8 | C2×D9 | semidirect |
| 129. C2×C8 | C2×D9 | semidirect |
| 149. C9 | #450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D9 | 2 |
| C2×C9×SD16 | 2 |
| #63508 | 2 |
| C2×#3675 | 2 |
| #63392 | 2 |
| #63380 | 2 |
| (C2×D9)⋊C8 | 2 |
| #5169 | 3 |