Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
818 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 818 conjugacy classes of subgroups — too many to draw. Only its 168 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 |
|---|---|---|
| 2. C32×#869 | C2 | semidirect |
| 3. C2×C3×#3715 | C2 | semidirect |
| 4. C3×C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 7. #10590375 | C3 | direct (N × H) |
| 23. C3×#869 | D3 | semidirect |
| 24. C3×#869 | C2×C3 | semidirect |
| 25. C2×#3715 | C2×C3 | semidirect |
| 26. C4×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 37. C3×C3⋊(C3⋊C8) | D4 | semidirect |
| 74. C33×C4 | SD16 | semidirect |
| 87. #869 | C3×D3 | semidirect |
| 126. C3⋊(C3⋊C8) | C3×D4 | semidirect |
| 188. C32×C4 | #214 | semidirect |
| 189. C32×C4 | #215 | semidirect |
| 190. C32×C4 | C3×SD16 | semidirect |
| 201. C33 | #492 | semidirect |
| 291. C3×C4 | #3715 | semidirect |
| 292. C3×C4 | C3×#214 | semidirect |
| 293. C3×C4 | C3×#215 | semidirect |
| 302. C32 | #5076 | semidirect |
| 303. C32 | #5085 | semidirect |
| 304. C32 | C3×#492 | semidirect |
| 335. C4 | C3×#3715 | semidirect |
| 341. C3 | #10590375 | direct (N × H) |
| 342. C3 | C3×#5076 | semidirect |
| 343. C3 | C3×#5085 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#874 | 2 |
| C32×#869 | 2 |
| C2×C3×#3715 | 2 |
| C3×C4×C3⋊(C3⋊C8) | 2 |
| C3×#5085 | 3 |
| C3×#5076 | 3 |
| #10590375 | 3 |