Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2412 conjugacy classes of subgroups; only the 452 normal subgroups are shown.
This group has 2412 conjugacy classes of subgroups — too many to draw. Only its 452 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. C22×#6308 | C2 | semidirect |
| 3. C22×C3×C3⋊(C3⋊C8) | C2 | semidirect |
| 4. C2×#88794 | C2 | direct (N × H) |
| 11. C2×#6308 | C22 | semidirect |
| 14. C2×C3×C3⋊(C3⋊C8) | C22 | semidirect |
| 15. #88794 | C22 | direct (N × H) |
| 22. C22×C3⋊(C3⋊C8) | D3 | semidirect |
| 32. #6308 | C23 | semidirect |
| 35. C3×C3⋊(C3⋊C8) | C23 | semidirect |
| 57. C2×C3⋊(C3⋊C8) | C2×D3 | semidirect |
| 60. C22×C33 | SD16 | semidirect |
| 102. C3⋊(C3⋊C8) | C22×D3 | semidirect |
| 105. C2×C33 | C2×SD16 | semidirect |
| 134. C22×C32 | #204 | semidirect |
| 135. C22×C32 | #214 | semidirect |
| 153. C33 | C22×SD16 | semidirect |
| 185. C2×C32 | C2×#204 | semidirect |
| 186. C2×C32 | C2×#214 | semidirect |
| 203. C22×C3 | #3716 | semidirect |
| 204. C22×C3 | #3754 | semidirect |
| 219. C32 | C22×#204 | semidirect |
| 220. C32 | C22×#214 | semidirect |
| 235. C2×C3 | C2×#3716 | semidirect |
| 236. C2×C3 | C2×#3754 | semidirect |
| 242. C22 | #88794 | direct (N × H) |
| 248. C3 | C22×#3716 | semidirect |
| 249. C3 | C22×#3754 | semidirect |
| 251. C2 | C2×#88794 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6308 | 2 |
| C22×C32×D12 | 2 |
| C22×C3×C3⋊(C3⋊C8) | 2 |
| C2×#88794 | 2 |
| C22×#3754 | 3 |
| C22×#3716 | 3 |