Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
984 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 198 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×#64153 | C2 | semidirect |
| 4. C2×C3×#3756 | C2 | semidirect |
| 7. C3×#63642 | C2 | semidirect |
| 8. #10592889 | C3 | direct (N × H) |
| 24. C2×C32×Q16 | D3 | semidirect |
| 25. C2×C32×Q16 | C2×C3 | semidirect |
| 27. #64153 | C2×C3 | semidirect |
| 28. C2×#3756 | C2×C3 | semidirect |
| 36. #63642 | C2×C3 | semidirect |
| 97. C2×C3×Q16 | C3×D3 | semidirect |
| 98. C2×C3×Q16 | C3⋊D3 | semidirect |
| 208. C2×Q16 | C3×C3⋊D3 | semidirect |
| 214. C33 | #497 | semidirect |
| 300. C32 | #5190 | semidirect |
| 301. C32 | C3×#497 | semidirect |
| 336. C3 | C3×#5190 | semidirect |
| 337. C3 | #10592889 | 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×#64156 | 2 |
| C3×#64153 | 2 |
| C2×C3×#3756 | 2 |
| C2×C3×#3755 | 2 |
| C2×C3×#3744 | 2 |
| C3×#63642 | 2 |
| #10592889 | 3 |
| C3×#5190 | 3 |