Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
820 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 166 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 |
|---|---|---|
| 192. C33 | #479 | semidirect |
| 268. C32 | #4829 | semidirect |
| 269. C32 | #5063 | semidirect |
| 300. C3 | #10590292 | semidirect |
| 301. C3 | #10592528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6308 | 2 |
| C3×#64079 | 2 |
| C32×C4⋊(C3⋊C8) | 2 |
| #11722055 | 2 |
| #11722052 | 2 |
| #11722042 | 2 |
| #10592528 | 3 |
| #10590292 | 3 |