Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
274 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 46 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 |
|---|---|---|
| 1. #11724362 | C2 | semidirect |
| 3. #11722805 | C2 | semidirect |
| 4. #11722803 | C2 | semidirect |
| 5. C3×#63746 | C2 | semidirect |
| 24. #63746 | D3 | semidirect |
| 137. C33 | #478 | semidirect |
| 203. C32 | #4891 | semidirect |
| 243. C3 | #10593557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724362 | 2 |
| #11724259 | 2 |
| #11722805 | 2 |
| #11722803 | 2 |
| C3×#63746 | 2 |
| #11722707 | 2 |
| #11722706 | 2 |
| #10593557 | 3 |
| #4891 | 9 |