Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
370 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 8. #63918 | C3 | direct (N × H) |
| 34. C33×C4 | Q8 | semidirect |
| 38. C32×Dic3 | Q8 | semidirect |
| 103. C32×C4 | Dic6 | semidirect |
| 104. C32×C4 | Dic6 | semidirect |
| 105. C32×C4 | C3×Q8 | semidirect |
| 115. C3×Dic3 | Dic6 | semidirect |
| 118. C3×Dic3 | C3×Q8 | semidirect |
| 120. C33 | C4⋊Q8 | semidirect |
| 194. C3×C4 | #627 | semidirect |
| 195. C3×C4 | C3×Dic6 | semidirect |
| 196. C3×C4 | C3×Dic6 | semidirect |
| 201. Dic3 | C3×Dic6 | semidirect |
| 207. C32 | #869 | semidirect |
| 208. C32 | #888 | semidirect |
| 209. C32 | C3×C4⋊Q8 | semidirect |
| 242. C4 | C3×#627 | semidirect |
| 247. C3 | #63918 | direct (N × H) |
| 248. C3 | C3×#869 | semidirect |
| 249. C3 | C3×#888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#627 | 2 |
| C3×C4⋊(C3⋊Dic3) | 2 |
| C32×C4⋊Dic3 | 2 |
| C32×C4×Dic3 | 2 |
| C3×Dic3⋊Dic3 | 2 |
| C3×#888 | 3 |
| C3×#869 | 3 |
| #63918 | 3 |