Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
474 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 474 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×#64121 | C2 | semidirect |
| 2. #11723654 | C2 | semidirect |
| 3. C3×#63654 | C2 | semidirect |
| 4. C3×#63653 | C2 | semidirect |
| 5. #11722069 | C2 | semidirect |
| 6. #11722068 | C2 | semidirect |
| 7. #11722065 | C2 | semidirect |
| 22. #64121 | D3 | semidirect |
| 29. #63654 | D3 | semidirect |
| 30. #63653 | D3 | semidirect |
| 275. C33 | #508 | semidirect |
| 395. C32 | #4912 | semidirect |
| 396. C32 | #4916 | semidirect |
| 397. C32 | #5194 | semidirect |
| 442. C3 | #10591032 | semidirect |
| 443. C3 | #10591034 | semidirect |
| 444. C3 | #10591035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64121 | 2 |
| #11723654 | 2 |
| C3×#63654 | 2 |
| C3×#63653 | 2 |
| #11722069 | 2 |
| #11722068 | 2 |
| #11722065 | 2 |
| #10591035 | 3 |
| #10591034 | 3 |
| #10591032 | 3 |