Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1512 conjugacy classes of subgroups; only the 413 normal subgroups are shown.
This group has 1512 conjugacy classes of subgroups — too many to draw. Only its 413 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 |
|---|---|---|
| 13. #88863 | C4 | semidirect |
| 115. C33 | #441 | semidirect |
| 153. C32 | #4789 | semidirect |
| 179. C3 | #10592488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C3⋊(C3⋊Dic3) | 2 |
| C2×#88863 | 2 |
| #11723928 | 2 |
| C33×#103 | 2 |
| #11722186 | 2 |
| #11722185 | 2 |
| #11722178 | 2 |
| #10592488 | 3 |