Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
470 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. #11720577 | C2 | semidirect |
| 3. #11720575 | C2 | semidirect |
| 6. C24×C3×C9 | C4 | semidirect |
| 10. C3×C9×C22⋊C4 | C4 | semidirect |
| 35. C24×C9 | Dic3 | semidirect |
| 43. C9×C22⋊C4 | Dic3 | semidirect |
| 93. C24×C3 | Dic9 | semidirect |
| 101. C3×C22⋊C4 | Dic9 | semidirect |
| 136. C3×C9 | AΣL(1,𝔽16) | semidirect |
| 169. C24 | C3⋊Dic9 | semidirect |
| 175. C22⋊C4 | C3⋊Dic9 | semidirect |
| 203. C9 | #4536 | semidirect |
| 238. C3 | #10588213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#120 | 2 |
| #11720577 | 2 |
| #11720575 | 2 |
| #10589402 | 3 |
| #10588213 | 3 |