Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
562 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×#88635 | C2 | semidirect |
| 2. C2×#88544 | C2 | semidirect |
| 3. C3×#63500 | C2 | semidirect |
| 4. C2×C9×#214 | C2 | semidirect |
| 5. #11720297 | C2 | semidirect |
| 6. #11720284 | C2 | semidirect |
| 7. (C2×D9)⋊(C3⋊C8) | C2 | semidirect |
| 34. #63500 | D3 | semidirect |
| 47. C4⋊(C3⋊D9) | D4 | semidirect |
| 55. C9×Dic6 | D4 | semidirect |
| 116. C2×#214 | D9 | semidirect |
| 261. C3×C9 | #449 | semidirect |
| 304. Dic6 | #611 | semidirect |
| 383. C9 | #5037 | semidirect |
| 437. C3 | #10588852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88635 | 2 |
| C2×#88544 | 2 |
| C3×#63500 | 2 |
| C2×C9×#214 | 2 |
| #11720297 | 2 |
| #11720284 | 2 |
| (C2×D9)⋊(C3⋊C8) | 2 |
| #10591521 | 3 |
| #10588852 | 3 |