Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
204 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 68 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. C3×#3701 | C2 | semidirect |
| 2. C3×C9×Q16 | C2 | semidirect |
| 3. C3×#3675 | C2 | semidirect |
| 4. C3×D72 | C2 | semidirect |
| 5. C3×C8×D9 | C2 | semidirect |
| 7. #63481 | C3 | direct (N × H) |
| 20. #3701 | C2×C3 | semidirect |
| 22. C9×Q16 | C2×C3 | semidirect |
| 23. #3675 | C2×C3 | semidirect |
| 24. D72 | C2×C3 | semidirect |
| 25. C8×D9 | C2×C3 | semidirect |
| 55. C3×Q16 | D9 | semidirect |
| 76. C3×C9 | #135 | semidirect |
| 101. Q16 | C3×D9 | semidirect |
| 119. C9 | C3×#135 | semidirect |
| 140. C3 | #63481 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3701 | 2 |
| C3×C9×Q16 | 2 |
| C3×#3675 | 2 |
| C3×D72 | 2 |
| C3×C8×D9 | 2 |
| C3×#919 | 3 |
| #63481 | 3 |