Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
990 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 990 conjugacy classes of subgroups — too many to draw. Only its 171 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. #11721837 | C2 | semidirect |
| 3. #11720577 | C2 | semidirect |
| 6. C23×C3⋊D9 | C22 | semidirect |
| 11. #88551 | C22 | semidirect |
| 15. C9×H(5,𝔽2) | D3 | semidirect |
| 20. C23×C3×C9 | D4 | semidirect |
| 28. C2×C3×C4×C9 | D4 | semidirect |
| 57. C3×H(5,𝔽2) | D9 | semidirect |
| 76. C23×C9 | #67 | semidirect |
| 84. C2×C4×C9 | #67 | semidirect |
| 126. H(5,𝔽2) | C3⋊D9 | semidirect |
| 129. C3×C9 | B(4,𝔽2) | semidirect |
| 132. C23×C3 | #611 | semidirect |
| 148. C2×C3×C4 | #611 | semidirect |
| 190. C9 | #5244 | semidirect |
| 194. C23 | #6233 | semidirect |
| 202. C2×C4 | #6233 | semidirect |
| 221. C3 | #10588924 | 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 |
| #11721837 | 2 |
| #11720577 | 2 |
| #10592943 | 3 |
| #10588924 | 3 |