Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
602 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 168 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 |
|---|---|---|
| 5. #10590312 | C3 | direct (N × H) |
| 25. C3×C3⋊(C3⋊C8) | Q8 | semidirect |
| 85. C3⋊(C3⋊C8) | C3×Q8 | semidirect |
| 139. C33 | #500 | semidirect |
| 213. C32 | #5078 | semidirect |
| 214. C32 | C3×#500 | semidirect |
| 244. C3 | #10590312 | direct (N × H) |
| 245. C3 | C3×#5078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#869 | 2 |
| C3×C4×C3⋊(C3⋊C8) | 2 |
| C3×#63576 | 2 |
| C3×#5078 | 3 |
| #10590312 | 3 |