Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
1036 conjugacy classes of subgroups; only the 321 normal subgroups are shown.
This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 321 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×C33×Q8 | C2 | semidirect |
| 4. C4⋊(C3⋊(C3⋊Dic3)) | C2 | semidirect |
| 5. #88857 | C2 | semidirect |
| 14. C2×C32×Q8 | D3 | semidirect |
| 22. C2×C3⋊(C3⋊D3) | Q8 | semidirect |
| 39. C2×C3×Q8 | C3⋊D3 | semidirect |
| 53. C33 | C22⋊Q8 | semidirect |
| 65. C2×Q8 | C3⋊(C3⋊D3) | semidirect |
| 78. C32 | #946 | semidirect |
| 98. C3 | #64155 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×Q8 | 2 |
| C2×C4×C3⋊(C3⋊D3) | 2 |
| #88859 | 2 |
| C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| #88857 | 2 |
| #64155 | 3 |