Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
390 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 95 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×#88521 | C2 | semidirect |
| 4. C3×#63377 | C2 | semidirect |
| 5. #11720277 | C2 | semidirect |
| 26. #63377 | D3 | semidirect |
| 158. C3×C9 | #470 | semidirect |
| 225. C9 | #4867 | semidirect |
| 254. C3 | #10588807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88521 | 2 |
| C2×C9×ΓL(1,𝔽25) | 2 |
| #11720961 | 2 |
| C3×#63377 | 2 |
| #11720277 | 2 |
| #10590853 | 3 |
| #10588807 | 3 |