Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
278 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 4. AGL(1,𝔽9)⋊Dic3 | C2 | semidirect |
| 5. #11724105 | C2 | semidirect |
| 115. C33 | #483 | semidirect |
| 175. C32 | #4721 | semidirect |
| 211. C3 | #10596415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724369 | 2 |
| C2×#88940 | 2 |
| C3×C22⋊AGL(1,𝔽9) | 2 |
| AGL(1,𝔽9)⋊Dic3 | 2 |
| #11724105 | 2 |
| #10596415 | 3 |
| #4721 | 9 |