Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
452 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 91 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. C3×#63500 | C2 | semidirect |
| 2. C2×C9×#213 | C2 | semidirect |
| 3. #11721036 | C2 | semidirect |
| 4. C2×D9×C3⋊C8 | C2 | semidirect |
| 5. #11720576 | C2 | semidirect |
| 6. #11720294 | C2 | semidirect |
| 7. #11720279 | C2 | semidirect |
| 32. #63500 | D3 | semidirect |
| 54. C9×C3⋊C8 | D4 | semidirect |
| 95. C2×C3×D9 | D8 | semidirect |
| 105. C2×#213 | D9 | semidirect |
| 220. C2×D9 | #213 | semidirect |
| 236. C3×C9 | #466 | semidirect |
| 276. C3⋊C8 | #611 | semidirect |
| 345. C9 | #5038 | semidirect |
| 395. C3 | #10588837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63500 | 2 |
| C2×C9×#213 | 2 |
| #11721036 | 2 |
| C2×D9×C3⋊C8 | 2 |
| #11720576 | 2 |
| #11720294 | 2 |
| #11720279 | 2 |
| #10591498 | 3 |
| #10588837 | 3 |