Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
386 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 69 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. #11721782 | C2 | semidirect |
| 2. #11720890 | C2 | semidirect |
| 3. C2×#88421 | C2 | semidirect |
| 4. #11720868 | C2 | semidirect |
| 5. C9×#823 | C2 | semidirect |
| 6. C3×#63383 | C2 | semidirect |
| 7. #11720286 | C2 | semidirect |
| 38. #63383 | D3 | semidirect |
| 114. #823 | D9 | semidirect |
| 228. C3×C9 | #472 | semidirect |
| 322. C9 | #4749 | semidirect |
| 362. C3 | #10588429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721782 | 2 |
| #11720890 | 2 |
| C2×#88421 | 2 |
| #11720868 | 2 |
| C9×#823 | 2 |
| C3×#63383 | 2 |
| #11720286 | 2 |
| #10590988 | 3 |
| #10588429 | 3 |