Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1250 conjugacy classes of subgroups; only the 257 normal subgroups are shown.
This group has 1250 conjugacy classes of subgroups — too many to draw. Only its 257 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×C4⋊(C3⋊D9) | C2 | semidirect |
| 2. C22×C3×D36 | C2 | semidirect |
| 3. C22×C9×C3⋊C8 | C2 | semidirect |
| 4. C2×#88417 | C2 | direct (N × H) |
| 11. C2×C4⋊(C3⋊D9) | C22 | semidirect |
| 13. C2×C3×D36 | C22 | semidirect |
| 14. C2×C9×C3⋊C8 | C22 | semidirect |
| 15. #88417 | C22 | direct (N × H) |
| 22. C22×D36 | D3 | semidirect |
| 33. C4⋊(C3⋊D9) | C23 | semidirect |
| 35. C3×D36 | C23 | semidirect |
| 36. C9×C3⋊C8 | C23 | semidirect |
| 58. C2×D36 | C2×D3 | semidirect |
| 61. C22×C3×C9 | D8 | semidirect |
| 76. C22×C3⋊C8 | D9 | semidirect |
| 107. D36 | C22×D3 | semidirect |
| 110. C2×C3×C9 | C2×D8 | semidirect |
| 134. C2×C3⋊C8 | C2×D9 | semidirect |
| 146. C22×C9 | #213 | semidirect |
| 162. C3×C9 | C22×D8 | semidirect |
| 193. C3⋊C8 | C22×D9 | semidirect |
| 200. C2×C9 | C2×#213 | semidirect |
| 218. C22×C3 | D72 | semidirect |
| 238. C9 | C22×#213 | semidirect |
| 254. C2×C3 | C2×D72 | semidirect |
| 266. C22 | #88417 | direct (N × H) |
| 271. C3 | C22×D72 | semidirect |
| 275. C2 | C2×#88417 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C3⋊D9) | 2 |
| C22×C3×D36 | 2 |
| C22×C9×C3⋊C8 | 2 |
| C2×#88417 | 2 |
| C22×#3714 | 3 |
| C22×D72 | 3 |