Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
732 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 166 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×C33×Q16 | C2 | semidirect |
| 3. C3×#63656 | C2 | semidirect |
| 4. C3×#63655 | C2 | semidirect |
| 5. C3×#63639 | C2 | semidirect |
| 6. #10592878 | C3 | direct (N × H) |
| 18. C2×C32×Q16 | D3 | semidirect |
| 19. C2×C32×Q16 | C2×C3 | semidirect |
| 22. #63656 | C2×C3 | semidirect |
| 23. #63655 | C2×C3 | semidirect |
| 24. #63639 | C2×C3 | semidirect |
| 70. C2×C3×Q16 | C3×D3 | semidirect |
| 71. C2×C3×Q16 | C3⋊D3 | semidirect |
| 148. C2×Q16 | C3×C3⋊D3 | semidirect |
| 152. C33 | #510 | semidirect |
| 213. C32 | #5179 | semidirect |
| 214. C32 | C3×#510 | semidirect |
| 240. C3 | C3×#5179 | semidirect |
| 241. C3 | #10592878 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×Q16 | 2 |
| C3×#64113 | 2 |
| C3×#63656 | 2 |
| C3×#63655 | 2 |
| C3×#63639 | 2 |
| #10592878 | 3 |
| C3×#5179 | 3 |