Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
940 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 940 conjugacy classes of subgroups — too many to draw. Only its 164 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. #11723967 | C2 | semidirect |
| 3. C32×#830 | C2 | semidirect |
| 4. #11722055 | C2 | semidirect |
| 5. #11722052 | C2 | semidirect |
| 6. #11722034 | C2 | semidirect |
| 7. #11722034 | C2 | semidirect |
| 31. C3×#830 | D3 | semidirect |
| 100. #830 | C3⋊D3 | semidirect |
| 217. C33 | #482 | semidirect |
| 314. C32 | #4737 | semidirect |
| 315. C32 | #5035 | semidirect |
| 358. C3 | #10591093 | semidirect |
| 359. C3 | #10592436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723967 | 2 |
| C3×#64139 | 2 |
| C32×#830 | 2 |
| #11722055 | 2 |
| #11722052 | 2 |
| #11722034 | 2 |
| #10592436 | 3 |
| #10591093 | 3 |