Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
434 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 101 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×C4⋊(C3⋊Dic9) | C2 | semidirect |
| 3. C3×#63389 | C2 | semidirect |
| 4. #11720295 | C2 | semidirect |
| 5. #11720262 | C2 | semidirect |
| 26. #63389 | D3 | semidirect |
| 175. C3×C9 | #480 | semidirect |
| 258. C9 | #4736 | semidirect |
| 296. C3 | #10588713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊Dic9) | 2 |
| C9×#930 | 2 |
| C3×#63389 | 2 |
| #11720295 | 2 |
| #11720262 | 2 |
| #10591094 | 3 |
| #10588713 | 3 |