Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
768 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 222 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. C32×#908 | C2 | semidirect |
| 2. C2×C32×D24 | C2 | semidirect |
| 3. C32×#901 | C2 | semidirect |
| 4. C33×#108 | C2 | semidirect |
| 5. C32×#823 | C2 | semidirect |
| 7. C3×#4897 | C3 | direct (N × H) |
| 22. C3×#908 | C2×C3 | semidirect |
| 23. C2×C3×D24 | C2×C3 | semidirect |
| 24. C3×#901 | C2×C3 | semidirect |
| 26. C32×#108 | D3 | semidirect |
| 27. C32×#108 | C2×C3 | semidirect |
| 29. C3×#823 | C2×C3 | semidirect |
| 43. #4897 | C32 | direct (N × H) |
| 78. #908 | C2×C32 | semidirect |
| 79. C2×D24 | C2×C32 | semidirect |
| 80. #901 | C2×C32 | semidirect |
| 82. C3×#108 | C3×D3 | semidirect |
| 83. C3×#108 | C2×C32 | semidirect |
| 85. #823 | C2×C32 | semidirect |
| 163. #108 | C32×D3 | semidirect |
| 165. C33 | #472 | semidirect |
| 233. C32 | #4897 | direct (N × H) |
| 234. C32 | C3×#472 | semidirect |
| 265. C3 | C3×#4897 | direct (N × H) |
| 266. C3 | C32×#472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#908 | 2 |
| C2×C32×D24 | 2 |
| C32×#901 | 2 |
| C33×#108 | 2 |
| C32×#823 | 2 |
| C32×#472 | 3 |
| C3×#4897 | 3 |