Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
546 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 216 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×C3×D4×C9 | C2 | semidirect |
| 2. C2×C3×#611 | C2 | semidirect |
| 3. C22×C3×Dic9 | C2 | semidirect |
| 4. C3×#3699 | C2 | direct (N × H) |
| 5. C2×C3×C4×D9 | C2 | semidirect |
| 6. C2×C3×Dic18 | C2 | semidirect |
| 8. C2×#3699 | C3 | direct (N × H) |
| 11. C3×D4×C9 | C22 | semidirect |
| 13. C3×#611 | C22 | semidirect |
| 16. C2×C3×Dic9 | C22 | semidirect |
| 17. C3×C4×D9 | C22 | semidirect |
| 18. C3×Dic18 | C22 | semidirect |
| 26. C2×D4×C9 | C2×C3 | semidirect |
| 27. C2×#611 | C2×C3 | semidirect |
| 28. C22×Dic9 | C2×C3 | semidirect |
| 29. #3699 | C2×C3 | direct (N × H) |
| 30. C2×C4×D9 | C2×C3 | semidirect |
| 31. C2×Dic18 | C2×C3 | semidirect |
| 56. D4×C9 | C22×C3 | semidirect |
| 59. #611 | C22×C3 | semidirect |
| 62. C2×Dic9 | C22×C3 | semidirect |
| 63. C4×D9 | C22×C3 | semidirect |
| 64. Dic18 | C22×C3 | semidirect |
| 66. C2×C3×C9 | #41 | semidirect |
| 73. C2×C3×D4 | D9 | semidirect |
| 103. C3×C9 | C2×#41 | semidirect |
| 112. C3×D4 | C2×D9 | semidirect |
| 135. C2×C9 | C3×#41 | semidirect |
| 141. C2×D4 | C3×D9 | semidirect |
| 166. C9 | C2×C3×#41 | semidirect |
| 171. D4 | C2×C3×D9 | semidirect |
| 183. C2×C3 | #3699 | direct (N × H) |
| 197. C3 | C2×#3699 | direct (N × H) |
| 201. C2 | C3×#3699 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×C9 | 2 |
| C2×C3×#611 | 2 |
| C22×C3×Dic9 | 2 |
| C3×#3699 | 2 |
| C2×C3×C4×D9 | 2 |
| C2×C3×Dic18 | 2 |
| C2×C3×#237 | 3 |
| C2×#3699 | 3 |