Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
498 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. C2×C9×#216 | C2 | semidirect |
| 3. #11720944 | C2 | semidirect |
| 4. C2×#88425 | C2 | semidirect |
| 5. #11720582 | C2 | semidirect |
| 6. #11720283 | C2 | semidirect |
| 7. (C2×D9)⋊(C3⋊C8) | C2 | semidirect |
| 111. C2×#216 | D9 | semidirect |
| 243. C3×C9 | #452 | semidirect |
| 349. C9 | #5239 | semidirect |
| 396. C3 | #10588867 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3701 | 2 |
| C2×C9×#216 | 2 |
| #11720944 | 2 |
| C2×#88425 | 2 |
| #11720582 | 2 |
| #11720283 | 2 |
| (C2×D9)⋊(C3⋊C8) | 2 |
| #10591597 | 3 |
| #10588867 | 3 |