Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
596 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 140 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×#6308 | C2 | semidirect |
| 3. C3×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 4. #88807 | C2 | semidirect |
| 21. C4⋊(C3⋊Dic3) | D3 | semidirect |
| 29. C2×C32×D3 | Q8 | semidirect |
| 76. C2×C3×D3 | Dic6 | semidirect |
| 88. C33 | C22⋊Q8 | semidirect |
| 130. C2×D3 | #634 | semidirect |
| 142. C32 | #897 | semidirect |
| 143. C32 | #924 | semidirect |
| 171. C3 | #63857 | semidirect |
| 172. C3 | #64133 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6308 | 2 |
| C2×C32×C4×D3 | 2 |
| C3×C4⋊(C3⋊Dic3) | 2 |
| #88807 | 2 |
| (C2×D3)⋊(C3⋊Dic3) | 2 |
| #64133 | 3 |
| #63857 | 3 |