Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1004 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 162 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 |
|---|---|---|
| 91. C3⋊(C3⋊Dic3) | Q16 | semidirect |
| 211. C33 | #494 | semidirect |
| 294. C32 | #5183 | semidirect |
| 295. C32 | #5183 | semidirect |
| 327. C3 | #10591628 | semidirect |
| 328. C3 | #10592882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723985 | 2 |
| C2×C3×#3756 | 2 |
| C2×C32×#216 | 2 |
| #11723451 | 2 |
| C2×#88800 | 2 |
| C2×#88799 | 2 |
| #11722018 | 2 |
| #10592882 | 3 |
| #10591628 | 3 |