Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
856 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 190 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 |
|---|---|---|
| 34. #6308 | Q8 | semidirect |
| 164. C33 | #477 | semidirect |
| 234. C32 | #4850 | semidirect |
| 235. C32 | #5091 | semidirect |
| 264. C3 | #10590284 | semidirect |
| 265. C3 | #10592790 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6308 | 2 |
| C32×#869 | 2 |
| C3×C4⋊(C3⋊(C3⋊C8)) | 2 |
| #11722057 | 2 |
| #11722041 | 2 |
| #10592790 | 3 |
| #10590284 | 3 |