Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
550 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 550 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 |
|---|---|---|
| 2. C2×C8×C3⋊D9 | C2 | semidirect |
| 3. #11720922 | C2 | semidirect |
| 4. C9×#821 | C2 | semidirect |
| 5. C3×#63376 | C2 | semidirect |
| 6. #11720294 | C2 | semidirect |
| 7. #11720268 | C2 | semidirect |
| 16. #88639 | C4 | semidirect |
| 37. #63376 | D3 | semidirect |
| 114. #821 | D9 | semidirect |
| 237. C3×C9 | #416 | semidirect |
| 342. C9 | #4804 | semidirect |
| 388. C3 | #10588452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88639 | 2 |
| C2×C8×C3⋊D9 | 2 |
| #11720922 | 2 |
| C9×#821 | 2 |
| C3×#63376 | 2 |
| #11720294 | 2 |
| #11720268 | 2 |
| #10590956 | 3 |
| #10588452 | 3 |