Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
446 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 87 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. #11721856 | C2 | semidirect |
| 2. C2×C9×#215 | C2 | semidirect |
| 4. C2×(C3⋊D9)⋊C8 | C2 | semidirect |
| 5. C3×#63395 | C2 | semidirect |
| 6. #11720295 | C2 | semidirect |
| 7. #11720278 | C2 | semidirect |
| 35. #63395 | D3 | semidirect |
| 52. C9×C3⋊C8 | D4 | semidirect |
| 90. C2×C3⋊D9 | SD16 | semidirect |
| 104. C2×#215 | D9 | semidirect |
| 235. C3×C9 | #465 | semidirect |
| 276. C3⋊C8 | #611 | semidirect |
| 341. C9 | #4807 | semidirect |
| 386. C3 | #10588851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721856 | 2 |
| C2×C9×#215 | 2 |
| #11721045 | 2 |
| C2×(C3⋊D9)⋊C8 | 2 |
| C3×#63395 | 2 |
| #11720295 | 2 |
| #11720278 | 2 |
| #10591591 | 3 |
| #10588851 | 3 |