Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
584 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 81 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. #11722673 | C2 | semidirect |
| 2. C9×#949 | C2 | semidirect |
| 3. #11720964 | C2 | semidirect |
| 4. #11720890 | C2 | semidirect |
| 5. C3×#63396 | C2 | semidirect |
| 6. #11720292 | C2 | semidirect |
| 7. #11720290 | C2 | semidirect |
| 39. #63396 | D3 | semidirect |
| 123. #949 | D9 | semidirect |
| 279. C3×C9 | #454 | semidirect |
| 403. C9 | #4827 | semidirect |
| 452. C3 | #10588881 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722673 | 2 |
| C9×#949 | 2 |
| #11720964 | 2 |
| #11720890 | 2 |
| C3×#63396 | 2 |
| #11720292 | 2 |
| #11720290 | 2 |
| #10591686 | 3 |
| #10588881 | 3 |