Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1284 conjugacy classes of subgroups; only the 306 normal subgroups are shown.
This group has 1284 conjugacy classes of subgroups — too many to draw. Only its 306 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 |
|---|---|---|
| 2. C2×C32×#214 | C2 | semidirect |
| 3. C32×#869 | C2 | semidirect |
| 4. C32×C4×C3⋊C8 | C2 | semidirect |
| 6. C3×#5076 | C3 | direct (N × H) |
| 19. C2×C3×#214 | C2×C3 | semidirect |
| 20. C3×#869 | C2×C3 | semidirect |
| 22. C3×C4×C3⋊C8 | C2×C3 | semidirect |
| 30. C32×C3⋊C8 | D4 | semidirect |
| 32. #5076 | C32 | direct (N × H) |
| 53. C33×C4 | SD16 | semidirect |
| 61. C2×#214 | C2×C32 | semidirect |
| 62. #869 | C2×C32 | semidirect |
| 64. C4×C3⋊C8 | C2×C32 | semidirect |
| 85. C3×C3⋊C8 | C3×D4 | semidirect |
| 119. C32×C4 | #214 | semidirect |
| 120. C32×C4 | C3×SD16 | semidirect |
| 128. C33 | #492 | semidirect |
| 149. C3⋊C8 | C32×D4 | semidirect |
| 178. C3×C4 | C3×#214 | semidirect |
| 179. C3×C4 | C32×SD16 | semidirect |
| 184. C32 | #5076 | direct (N × H) |
| 185. C32 | C3×#492 | semidirect |
| 207. C4 | C32×#214 | semidirect |
| 210. C3 | C3×#5076 | direct (N × H) |
| 211. C3 | C32×#492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#127 | 2 |
| C2×C32×#214 | 2 |
| C32×#869 | 2 |
| C32×C4×C3⋊C8 | 2 |
| C32×#492 | 3 |
| C3×#5076 | 3 |