Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
780 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 190 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×#63655 | C2 | direct (N × H) |
| 4. C2×C3×C3⋊(C3⋊C16) | C2 | semidirect |
| 5. C2×#63655 | C3 | direct (N × H) |
| 10. C33×Q16 | C22 | semidirect |
| 14. C3×C3⋊(C3⋊C16) | C22 | semidirect |
| 16. C2×C32×Q16 | D3 | semidirect |
| 17. C2×C32×Q16 | C2×C3 | semidirect |
| 20. #63655 | C2×C3 | direct (N × H) |
| 21. C2×C3⋊(C3⋊C16) | C2×C3 | semidirect |
| 44. C32×Q16 | C2×D3 | semidirect |
| 45. C32×Q16 | C22×C3 | semidirect |
| 53. C3⋊(C3⋊C16) | C22×C3 | semidirect |
| 62. C2×C3×Q16 | C3×D3 | semidirect |
| 63. C2×C3×Q16 | C3⋊D3 | semidirect |
| 95. C2×C33 | SD32 | semidirect |
| 107. C3×Q16 | C2×C3×D3 | semidirect |
| 108. C3×Q16 | C2×C3⋊D3 | semidirect |
| 134. C2×Q16 | C3×C3⋊D3 | semidirect |
| 138. C33 | C2×SD32 | semidirect |
| 165. C2×C32 | #828 | semidirect |
| 166. C2×C32 | C3×SD32 | semidirect |
| 174. Q16 | C2×C3×C3⋊D3 | semidirect |
| 196. C32 | C2×#828 | semidirect |
| 197. C32 | C2×C3×SD32 | semidirect |
| 210. C2×C3 | C3×#828 | semidirect |
| 211. C2×C3 | #63655 | direct (N × H) |
| 222. C3 | C2×C3×#828 | semidirect |
| 223. C3 | C2×#63655 | direct (N × H) |
| 225. C2 | C3×#63655 | 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 |
| C2×C3×#3745 | 2 |
| C3×#63655 | 2 |
| C2×C3×C3⋊(C3⋊C16) | 2 |
| C2×#63655 | 3 |
| C2×C3×#828 | 3 |