Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
800 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 200 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 |
|---|---|---|
| 66. C33×C4 | Q16 | semidirect |
| 146. C32×C4 | #216 | semidirect |
| 147. C32×C4 | #216 | semidirect |
| 161. C33 | #462 | semidirect |
| 219. C3×C4 | #3718 | semidirect |
| 220. C3×C4 | #3756 | semidirect |
| 229. C32 | #5031 | semidirect |
| 230. C32 | #5090 | semidirect |
| 256. C4 | #88798 | semidirect |
| 260. C3 | #10590384 | semidirect |
| 261. C3 | #10592730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64078 | 2 |
| C32×C4×Dic6 | 2 |
| C2×#88798 | 2 |
| C4⋊(C3⋊(C3⋊(C3⋊C8))) | 2 |
| #11722039 | 2 |
| #10592730 | 3 |
| #10590384 | 3 |