Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
670 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 129 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. C3×C9×H(5,𝔽2) | C2 | semidirect |
| 2. C9×#949 | C2 | semidirect |
| 3. C9×#940 | C2 | semidirect |
| 4. C9×#837 | C2 | semidirect |
| 5. C9×#833 | C2 | semidirect |
| 14. C2×C9×D12 | C22 | semidirect |
| 17. C4×C9×Dic3 | C22 | semidirect |
| 18. C9×#208 | C22 | semidirect |
| 23. C9×H(5,𝔽2) | D3 | semidirect |
| 33. C3×Q8×C9 | D4 | semidirect |
| 37. C3×D4×C9 | D4 | semidirect |
| 46. #5241 | C9 | direct (N × H) |
| 85. C3×H(5,𝔽2) | C2×C9 | semidirect |
| 89. #949 | C2×C9 | semidirect |
| 90. #940 | C2×C9 | semidirect |
| 93. #837 | C2×C9 | semidirect |
| 94. #833 | C2×C9 | semidirect |
| 116. Q8×C9 | #67 | semidirect |
| 126. D4×C9 | #67 | semidirect |
| 159. C2×D12 | C22×C9 | semidirect |
| 166. C4×Dic3 | C22×C9 | semidirect |
| 167. #208 | C22×C9 | semidirect |
| 195. H(5,𝔽2) | D3×C9 | semidirect |
| 200. C3×C9 | #453 | semidirect |
| 210. C3×Q8 | D4×C9 | semidirect |
| 224. C3×D4 | D4×C9 | semidirect |
| 295. C9 | #5241 | direct (N × H) |
| 299. Q8 | C9×#67 | semidirect |
| 305. D4 | C9×#67 | semidirect |
| 336. C3 | C9×#453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×H(5,𝔽2) | 2 |
| C9×#949 | 2 |
| C9×#940 | 2 |
| C9×#837 | 2 |
| C9×#833 | 2 |
| C3×#5241 | 3 |
| C9×#453 | 3 |