Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
466 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 71 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. C3×#64128 | C2 | semidirect |
| 2. #11723654 | C2 | semidirect |
| 3. C3×#63656 | C2 | semidirect |
| 4. C3×#63655 | C2 | semidirect |
| 5. #11722068 | C2 | semidirect |
| 6. #11722067 | C2 | semidirect |
| 7. #11722065 | C2 | semidirect |
| 22. #64128 | D3 | semidirect |
| 29. #63656 | D3 | semidirect |
| 30. #63655 | D3 | semidirect |
| 275. C33 | #508 | semidirect |
| 392. C32 | #4916 | semidirect |
| 393. C32 | #4919 | semidirect |
| 394. C32 | #5194 | semidirect |
| 436. C3 | #10591046 | semidirect |
| 437. C3 | #10591048 | semidirect |
| 438. C3 | #10591049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64128 | 2 |
| #11723654 | 2 |
| C3×#63656 | 2 |
| C3×#63655 | 2 |
| #11722068 | 2 |
| #11722067 | 2 |
| #11722065 | 2 |
| #10591049 | 3 |
| #10591048 | 3 |
| #10591046 | 3 |