Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
900 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 900 conjugacy classes of subgroups — too many to draw. Only its 194 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 |
| 4. C3×#63662 | C2 | semidirect |
| 5. C3×#63644 | C2 | semidirect |
| 6. #10592888 | C3 | direct (N × H) |
| 18. C2×C32×Q16 | D3 | semidirect |
| 19. C2×C32×Q16 | C2×C3 | semidirect |
| 24. #63662 | C2×C3 | semidirect |
| 25. #63644 | C2×C3 | semidirect |
| 71. C2×C3×Q16 | C3×D3 | semidirect |
| 72. C2×C3×Q16 | C3⋊D3 | semidirect |
| 153. C2×Q16 | C3×C3⋊D3 | semidirect |
| 158. C33 | #470 | semidirect |
| 224. C32 | #5189 | semidirect |
| 225. C32 | C3×#470 | semidirect |
| 254. C3 | C3×#5189 | semidirect |
| 255. C3 | #10592888 | 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×#64155 | 2 |
| C2×C3×#3743 | 2 |
| C3×#63662 | 2 |
| C3×#63644 | 2 |
| #10592888 | 3 |
| C3×#5189 | 3 |