Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1456 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1456 conjugacy classes of subgroups — too many to draw. Only its 349 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. #11723950 | C2 | semidirect |
| 3. C2×#88851 | C2 | semidirect |
| 4. #11723942 | C2 | semidirect |
| 5. C33×#108 | C2 | semidirect |
| 6. #11722194 | C2 | semidirect |
| 7. #11722193 | C2 | semidirect |
| 28. C32×#108 | D3 | semidirect |
| 75. C3×#108 | C3⋊D3 | semidirect |
| 126. #108 | C3⋊(C3⋊D3) | semidirect |
| 129. C33 | #471 | semidirect |
| 173. C32 | #4898 | semidirect |
| 202. C3 | #10592597 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723950 | 2 |
| #11723949 | 2 |
| C2×#88851 | 2 |
| #11723942 | 2 |
| C33×#108 | 2 |
| #11722194 | 2 |
| #11722193 | 2 |
| #10592597 | 3 |