Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
596 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 94 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. C2×#88800 | C2 | semidirect |
| 5. #11722074 | C2 | semidirect |
| 6. #11722030 | C2 | semidirect |
| 7. C3×#63577 | C2 | semidirect |
| 43. #63577 | D3 | semidirect |
| 345. C33 | #473 | semidirect |
| 499. C32 | #4896 | semidirect |
| 500. C32 | #5143 | semidirect |
| 501. C32 | #5204 | semidirect |
| 547. C3 | #10590932 | semidirect |
| 548. C3 | #10590983 | semidirect |
| 549. C3 | #10591682 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88800 | 2 |
| #11723379 | 2 |
| C3×#63831 | 2 |
| C3×#63814 | 2 |
| #11722074 | 2 |
| #11722030 | 2 |
| C3×#63577 | 2 |
| #10591682 | 3 |
| #10590983 | 3 |
| #10590932 | 3 |