Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2940 conjugacy classes of subgroups; only the 851 normal subgroups are shown.
This group has 2940 conjugacy classes of subgroups — too many to draw. Only its 851 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 |
|---|---|---|
| 2. C2×#88864 | C2 | semidirect |
| 3. #11722204 | C2 | direct (N × H) |
| 5. C24×C33 | C4 | semidirect |
| 9. C2×C33×D4 | C4 | semidirect |
| 11. C22×C33×C4 | C4 | semidirect |
| 14. #88864 | C22 | semidirect |
| 24. C23×C33 | C2×C4 | semidirect |
| 32. C2×C33×C4 | C2×C4 | semidirect |
| 36. C24×C32 | Dic3 | semidirect |
| 40. C2×C32×D4 | Dic3 | semidirect |
| 42. C22×C32×C4 | Dic3 | semidirect |
| 71. C23×C32 | C2×Dic3 | semidirect |
| 79. C2×C32×C4 | C2×Dic3 | semidirect |
| 88. C2×C33 | #99 | semidirect |
| 90. C24×C3 | C3⋊Dic3 | semidirect |
| 94. C2×C3×D4 | C3⋊Dic3 | semidirect |
| 96. C22×C3×C4 | C3⋊Dic3 | semidirect |
| 119. C33 | C2×#99 | semidirect |
| 126. C23×C3 | C2×C3⋊Dic3 | semidirect |
| 134. C2×C3×C4 | C2×C3⋊Dic3 | semidirect |
| 142. C2×C32 | #834 | semidirect |
| 144. C24 | C3⋊(C3⋊Dic3) | semidirect |
| 148. C2×D4 | C3⋊(C3⋊Dic3) | semidirect |
| 151. C22×C4 | C3⋊(C3⋊Dic3) | semidirect |
| 170. C32 | C2×#834 | semidirect |
| 177. C23 | C2×C3⋊(C3⋊Dic3) | semidirect |
| 187. C2×C4 | C2×C3⋊(C3⋊Dic3) | semidirect |
| 193. C2×C3 | #63661 | semidirect |
| 211. C3 | C2×#63661 | semidirect |
| 217. C2 | #11722204 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×D4 | 2 |
| C2×#88864 | 2 |
| #11722204 | 2 |
| C2×#63661 | 3 |