Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1124 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 1124 conjugacy classes of subgroups — too many to draw. Only its 164 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 |
|---|---|---|
| 2. #11723985 | C2 | semidirect |
| 3. #11723379 | C2 | semidirect |
| 4. C3×#63663 | C2 | semidirect |
| 5. #11722043 | C2 | semidirect |
| 27. #63663 | D3 | semidirect |
| 178. C33 | #456 | semidirect |
| 252. C32 | #4752 | semidirect |
| 253. C32 | #5246 | semidirect |
| 284. C3 | #10591649 | semidirect |
| 285. C3 | #10592945 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#1007 | 2 |
| #11723985 | 2 |
| #11723379 | 2 |
| C3×#63663 | 2 |
| #11722043 | 2 |
| #10592945 | 3 |
| #10591649 | 3 |