Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
456 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 456 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×Q16×C3⋊D3 | C2 | semidirect |
| 3. C3×#63656 | C2 | semidirect |
| 4. C3×#63655 | C2 | semidirect |
| 5. #11722069 | C2 | semidirect |
| 6. #11722068 | C2 | semidirect |
| 7. #11722066 | C2 | semidirect |
| 22. Q16×C3⋊D3 | D3 | semidirect |
| 29. #63656 | D3 | semidirect |
| 30. #63655 | D3 | semidirect |
| 274. C33 | #510 | semidirect |
| 387. C32 | #4915 | semidirect |
| 388. C32 | #4918 | semidirect |
| 389. C32 | #5179 | semidirect |
| 427. C3 | #10591045 | semidirect |
| 428. C3 | #10591047 | semidirect |
| 429. C3 | #10591050 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q16×C3⋊D3 | 2 |
| #11723654 | 2 |
| C3×#63656 | 2 |
| C3×#63655 | 2 |
| #11722069 | 2 |
| #11722068 | 2 |
| #11722066 | 2 |
| #10591050 | 3 |
| #10591047 | 3 |
| #10591045 | 3 |