Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
424 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 96 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. C23×C3×D9 | C2 | semidirect |
| 2. C2×C3×#611 | C2 | semidirect |
| 3. C2×C3×D36 | C2 | semidirect |
| 4. C3×C9×C22⋊C4 | C2 | semidirect |
| 5. C3×(C2×D9)⋊C4 | C2 | semidirect |
| 7. #63444 | C3 | direct (N × H) |
| 12. C22×C3×D9 | C22 | semidirect |
| 13. C2×C3×C4×C9 | C22 | semidirect |
| 15. C2×C3×Dic9 | C22 | semidirect |
| 20. C23×D9 | C2×C3 | semidirect |
| 23. C2×#611 | C2×C3 | semidirect |
| 24. C2×D36 | C2×C3 | semidirect |
| 26. C9×C22⋊C4 | C2×C3 | semidirect |
| 27. (C2×D9)⋊C4 | C2×C3 | semidirect |
| 29. C22×C3×C9 | D4 | semidirect |
| 36. C2×C3×D9 | D4 | semidirect |
| 55. C22×D9 | C22×C3 | semidirect |
| 57. C2×C4×C9 | C22×C3 | semidirect |
| 59. C2×Dic9 | C22×C3 | semidirect |
| 74. C3×C22⋊C4 | D9 | semidirect |
| 92. C22×C9 | C3×D4 | semidirect |
| 99. C2×D9 | C3×D4 | semidirect |
| 104. C3×C9 | #120 | semidirect |
| 120. C2×C3×C4 | C2×D9 | semidirect |
| 142. C22⋊C4 | C3×D9 | semidirect |
| 154. C22×C3 | D36 | semidirect |
| 171. C9 | C3×#120 | semidirect |
| 180. C2×C4 | C2×C3×D9 | semidirect |
| 201. C22 | C3×D36 | semidirect |
| 206. C3 | #63444 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D9 | 2 |
| C2×C3×#611 | 2 |
| C2×C3×D36 | 2 |
| C3×C9×C22⋊C4 | 2 |
| C3×(C2×D9)⋊C4 | 2 |
| C3×#882 | 3 |
| #63444 | 3 |