Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
458 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 118 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×C9×M16 | C2 | semidirect |
| 2. C3×#63492 | C2 | semidirect |
| 3. C2×C3×D72 | C2 | semidirect |
| 4. C3×#63380 | C2 | semidirect |
| 5. C3×#63377 | C2 | semidirect |
| 7. #10588817 | C3 | direct (N × H) |
| 23. C2×C9×M16 | C2×C3 | semidirect |
| 24. #63492 | C2×C3 | semidirect |
| 25. C2×D72 | C2×C3 | semidirect |
| 26. #63380 | C2×C3 | semidirect |
| 27. #63377 | C2×C3 | semidirect |
| 39. C3×C8×C9 | D4 | semidirect |
| 76. C2×C3×M16 | D9 | semidirect |
| 115. C8×C9 | C3×D4 | semidirect |
| 170. C2×M16 | C3×D9 | semidirect |
| 174. C3×C9 | #469 | semidirect |
| 204. C3×C8 | #611 | semidirect |
| 254. C9 | C3×#469 | semidirect |
| 266. C8 | C3×#611 | semidirect |
| 289. C3 | #10588817 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9×M16 | 2 |
| C3×#63492 | 2 |
| C2×C3×D72 | 2 |
| C3×#63380 | 2 |
| C3×#63377 | 2 |
| C3×#5135 | 3 |
| #10588817 | 3 |