Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
513 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 513 conjugacy classes of subgroups — too many to draw. Only its 149 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×C4×D9 | C2 | semidirect |
| 3. C2×C9×C4⋊C4 | C2 | semidirect |
| 4. C2×(C2×D9)⋊C4 | C2 | semidirect |
| 5. C2×(C2×D9)⋊C4 | C2 | semidirect |
| 6. C2×(C2×D9)⋊C4 | C2 | semidirect |
| 7. C2×Dic9⋊C4 | C2 | semidirect |
| 8. #63456 | C2 | direct (N × H) |
| 20. C2×C4×D9 | C22 | semidirect |
| 21. C9×C4⋊C4 | C22 | semidirect |
| 22. (C2×D9)⋊C4 | C22 | semidirect |
| 23. (C2×D9)⋊C4 | C22 | semidirect |
| 24. (C2×D9)⋊C4 | C22 | semidirect |
| 25. Dic9⋊C4 | C22 | semidirect |
| 93. C2×C4⋊C4 | D9 | semidirect |
| 118. C2×C9 | #123 | semidirect |
| 136. C4⋊C4 | C2×D9 | semidirect |
| 157. C9 | C2×#123 | semidirect |
| 205. C2 | #63456 | 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×C4×D9 | 2 |
| C2×C9×C4⋊C4 | 2 |
| C2×(C2×D9)⋊C4 | 2 |
| C2×Dic9⋊C4 | 2 |
| #63456 | 2 |
| C2×#894 | 3 |