Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
440 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 89 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. #11721854 | C2 | semidirect |
| 2. C2×C9×#216 | C2 | semidirect |
| 5. C2×#88428 | C2 | semidirect |
| 7. #11720275 | C2 | semidirect |
| 102. C2×#216 | D9 | semidirect |
| 215. C3×C9 | #497 | semidirect |
| 303. C9 | #5167 | semidirect |
| 338. C3 | #10588870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721854 | 2 |
| C2×C9×#216 | 2 |
| C2×C3×#3675 | 2 |
| #11720951 | 2 |
| C2×#88428 | 2 |
| C2×#88415 | 2 |
| #11720275 | 2 |
| #10591611 | 3 |
| #10588870 | 3 |