Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
866 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 866 conjugacy classes of subgroups — too many to draw. Only its 144 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×C32×D24 | C2 | semidirect |
| 2. C3×#63914 | C2 | semidirect |
| 3. C2×C3×#3713 | C2 | semidirect |
| 4. C3×C8×C3⋊Dic3 | C2 | semidirect |
| 6. #10590886 | C3 | direct (N × H) |
| 18. C2×C3×D24 | D3 | semidirect |
| 19. C2×C3×D24 | C2×C3 | semidirect |
| 20. #63914 | C2×C3 | semidirect |
| 21. C2×#3713 | C2×C3 | semidirect |
| 22. C8×C3⋊Dic3 | C2×C3 | semidirect |
| 31. C33×C8 | D4 | semidirect |
| 32. C3×C3⋊(C3⋊C8) | D4 | semidirect |
| 63. C3×C3⋊Dic3 | D8 | semidirect |
| 71. C2×D24 | C3×D3 | semidirect |
| 100. C32×C8 | #67 | semidirect |
| 101. C32×C8 | C3×D4 | semidirect |
| 102. C3⋊(C3⋊C8) | C3×D4 | semidirect |
| 155. C3⋊Dic3 | C3×D8 | semidirect |
| 162. C33 | #493 | semidirect |
| 189. C3×C8 | #625 | semidirect |
| 190. C3×C8 | C3×#67 | semidirect |
| 243. C32 | #5151 | semidirect |
| 244. C32 | C3×#493 | semidirect |
| 252. C8 | C3×#625 | semidirect |
| 276. C3 | #10590886 | direct (N × H) |
| 277. C3 | C3×#5151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D24 | 2 |
| C3×#63914 | 2 |
| C2×C3×#3713 | 2 |
| C3×C8×C3⋊Dic3 | 2 |
| C3×#5151 | 3 |
| #10590886 | 3 |