Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
646 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 646 conjugacy classes of subgroups — too many to draw. Only its 85 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×#63710 | C2 | semidirect |
| 2. C9×#937 | C2 | semidirect |
| 3. #11721286 | C2 | semidirect |
| 4. #11720577 | C2 | semidirect |
| 5. #11720329 | C2 | semidirect |
| 8. C23×D3×C9 | C22 | semidirect |
| 17. #88551 | C22 | semidirect |
| 18. C9×#217 | C22 | semidirect |
| 24. #63710 | D3 | semidirect |
| 32. C23×C3×C9 | D4 | semidirect |
| 38. C22×C3×D9 | D4 | semidirect |
| 40. C2×C3×C4×C9 | D4 | semidirect |
| 48. C2×C3×Dic9 | D4 | semidirect |
| 105. #937 | D9 | semidirect |
| 137. C23×C9 | #67 | semidirect |
| 140. C22×D9 | #67 | semidirect |
| 146. C2×C4×C9 | #67 | semidirect |
| 154. C2×Dic9 | #67 | semidirect |
| 166. C23×D3 | C2×D9 | semidirect |
| 190. #217 | C2×D9 | semidirect |
| 239. C3×C9 | B(4,𝔽2) | semidirect |
| 247. C23×C3 | #611 | semidirect |
| 270. C2×C3×C4 | #611 | semidirect |
| 359. C9 | #5244 | semidirect |
| 365. C23 | #6194 | semidirect |
| 380. C2×C4 | #6194 | semidirect |
| 415. C3 | #10588712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63710 | 2 |
| C9×#937 | 2 |
| #11721286 | 2 |
| #11720577 | 2 |
| #11720329 | 2 |
| #10591530 | 3 |
| #10588712 | 3 |