Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
546 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 143 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×C4×C3⋊D9 | C2 | semidirect |
| 2. C2×C9×D12 | C2 | semidirect |
| 3. C2×C3×Dic18 | C2 | semidirect |
| 4. C2×#6195 | C2 | semidirect |
| 5. C2×D3×Dic9 | C2 | semidirect |
| 6. #88639 | C2 | direct (N × H) |
| 13. C4×C3⋊D9 | C22 | semidirect |
| 15. C9×D12 | C22 | semidirect |
| 16. C3×Dic18 | C22 | semidirect |
| 17. #6195 | C22 | semidirect |
| 18. D3×Dic9 | C22 | semidirect |
| 31. C2×Dic18 | D3 | semidirect |
| 65. Dic18 | C2×D3 | semidirect |
| 66. C2×C3×C9 | #41 | semidirect |
| 77. C2×D12 | D9 | semidirect |
| 105. C3×C9 | C2×#41 | semidirect |
| 124. D12 | C2×D9 | semidirect |
| 137. C2×C9 | #239 | semidirect |
| 170. C9 | C2×#239 | semidirect |
| 184. C2×C3 | #3699 | semidirect |
| 201. C3 | C2×#3699 | semidirect |
| 205. C2 | #88639 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊D9 | 2 |
| C2×C9×D12 | 2 |
| C2×C3×Dic18 | 2 |
| C2×#6195 | 2 |
| C2×D3×Dic9 | 2 |
| #88639 | 2 |
| C2×#3796 | 3 |
| C2×#3699 | 3 |