Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
4060 conjugacy classes of subgroups; only the 1131 normal subgroups are shown.
This group has 4060 conjugacy classes of subgroups — too many to draw. Only its 1131 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 |
|---|---|---|
| 6. #11723929 | C2 | direct (N × H) |
| 27. C2×C33×C4 | Q8 | semidirect |
| 32. C2×C3⋊(C3⋊Dic3) | Q8 | semidirect |
| 54. C33×C4 | C2×Q8 | semidirect |
| 57. C3⋊(C3⋊Dic3) | C2×Q8 | semidirect |
| 66. C2×C32×C4 | Dic6 | semidirect |
| 77. C2×C33 | C4⋊Q8 | semidirect |
| 97. C32×C4 | C2×Dic6 | semidirect |
| 107. C33 | C2×C4⋊Q8 | semidirect |
| 110. C2×C3×C4 | #634 | semidirect |
| 120. C2×C32 | #888 | semidirect |
| 140. C3×C4 | C2×#634 | semidirect |
| 144. C32 | C2×#888 | semidirect |
| 154. C2×C4 | #6308 | semidirect |
| 157. C2×C3 | #64097 | semidirect |
| 169. C4 | C2×#6308 | semidirect |
| 170. C3 | C2×#64097 | semidirect |
| 171. C2 | #11723929 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6308 | 2 |
| C2×C33×C4⋊C4 | 2 |
| C2×C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| C2×#88857 | 2 |
| C2×C4×C3⋊(C3⋊Dic3) | 2 |
| #11723929 | 2 |
| C2×#64097 | 3 |