Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
472 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 130 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×C3×D72 | C2 | semidirect |
| 2. C2×C3×#3664 | C2 | semidirect |
| 3. C3×#63437 | C2 | semidirect |
| 4. C3×#63436 | C2 | semidirect |
| 5. C3×C9×#97 | C2 | semidirect |
| 7. #10588393 | C3 | direct (N × H) |
| 22. C2×D72 | C2×C3 | semidirect |
| 23. C2×#3664 | C2×C3 | semidirect |
| 24. #63437 | C2×C3 | semidirect |
| 25. #63436 | C2×C3 | semidirect |
| 27. C9×#97 | C2×C3 | semidirect |
| 38. C3×C8×C9 | D4 | semidirect |
| 78. C3×#97 | D9 | semidirect |
| 104. C8×C9 | C3×D4 | semidirect |
| 153. #97 | C3×D9 | semidirect |
| 154. C3×C9 | #496 | semidirect |
| 178. C3×C8 | D36 | semidirect |
| 220. C9 | C3×#496 | semidirect |
| 231. C8 | C3×D36 | semidirect |
| 251. C3 | #10588393 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D72 | 2 |
| C2×C3×#3664 | 2 |
| C3×#63437 | 2 |
| C3×#63436 | 2 |
| C3×C9×#97 | 2 |
| C3×#4712 | 3 |
| #10588393 | 3 |