Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
916 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 916 conjugacy classes of subgroups — too many to draw. Only its 186 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. C32×C3⋊#95 | C2 | semidirect |
| 3. C32×#830 | C2 | semidirect |
| 5. C3×#4537 | C3 | direct (N × H) |
| 7. C2×C33×D4 | C4 | semidirect |
| 10. C33×C4⋊C4 | C4 | semidirect |
| 18. C3×C3⋊#95 | C2×C3 | semidirect |
| 19. C3×#830 | C2×C3 | semidirect |
| 34. #4537 | C32 | direct (N × H) |
| 39. C2×C32×D4 | Dic3 | semidirect |
| 40. C2×C32×D4 | C3×C4 | semidirect |
| 48. C32×C4⋊C4 | Dic3 | semidirect |
| 49. C32×C4⋊C4 | C3×C4 | semidirect |
| 71. C3⋊#95 | C2×C32 | semidirect |
| 72. #830 | C2×C32 | semidirect |
| 119. C2×C3×D4 | C3×Dic3 | semidirect |
| 120. C2×C3×D4 | C32×C4 | semidirect |
| 128. C3×C4⋊C4 | C3×Dic3 | semidirect |
| 129. C3×C4⋊C4 | C32×C4 | semidirect |
| 172. C33 | #327 | semidirect |
| 227. C2×D4 | C32×Dic3 | semidirect |
| 231. C4⋊C4 | C32×Dic3 | semidirect |
| 269. C32 | #4537 | direct (N × H) |
| 270. C32 | C3×#327 | semidirect |
| 315. C3 | C3×#4537 | direct (N × H) |
| 316. C3 | C32×#327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#121 | 2 |
| C32×C3⋊#95 | 2 |
| C32×#830 | 2 |
| C32×#327 | 3 |
| C3×#4537 | 3 |