Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1540 conjugacy classes of subgroups; only the 523 normal subgroups are shown.
This group has 1540 conjugacy classes of subgroups — too many to draw. Only its 523 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 |
|---|---|---|
| 15. #88863 | C4 | direct (N × H) |
| 58. C33×C4 | Q16 | semidirect |
| 103. C32×C4 | #216 | semidirect |
| 115. C33 | C4×Q16 | semidirect |
| 148. C3×C4 | #3756 | semidirect |
| 153. C32 | C4×#216 | semidirect |
| 176. C4 | #88863 | direct (N × H) |
| 179. C3 | C4×#3756 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4×Q8 | 2 |
| C2×#88863 | 2 |
| C4×#6308 | 2 |
| #11722205 | 2 |
| #11722180 | 2 |
| #11722177 | 2 |
| C4×C3⋊(C3⋊(C3⋊C8)) | 2 |
| C4×#3756 | 3 |