Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
646 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 646 conjugacy classes of subgroups — too many to draw. Only its 89 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. C9×#1004 | C2 | semidirect |
| 2. C3×#63499 | C2 | semidirect |
| 3. #11721285 | C2 | semidirect |
| 4. #11720577 | C2 | semidirect |
| 5. #11720332 | C2 | semidirect |
| 8. C23×C3×D9 | C22 | semidirect |
| 17. #88551 | C22 | semidirect |
| 18. C3×#3676 | C22 | semidirect |
| 28. #63499 | D3 | semidirect |
| 32. C23×C3×C9 | D4 | semidirect |
| 35. C22×D3×C9 | D4 | semidirect |
| 40. C2×C3×C4×C9 | D4 | semidirect |
| 47. C2×C9×Dic3 | D4 | semidirect |
| 64. C23×D9 | C2×D3 | semidirect |
| 80. #3676 | C2×D3 | semidirect |
| 101. #1004 | D9 | semidirect |
| 136. C23×C9 | #67 | semidirect |
| 152. C2×C4×C9 | #67 | semidirect |
| 239. C3×C9 | B(4,𝔽2) | semidirect |
| 247. C23×C3 | #611 | semidirect |
| 255. C22×D3 | #611 | semidirect |
| 270. C2×C3×C4 | #611 | semidirect |
| 283. C2×Dic3 | #611 | semidirect |
| 359. C9 | #5032 | semidirect |
| 365. C23 | #6194 | semidirect |
| 380. C2×C4 | #6194 | semidirect |
| 415. C3 | #10588924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#1004 | 2 |
| C3×#63499 | 2 |
| #11721285 | 2 |
| #11720577 | 2 |
| #11720332 | 2 |
| #10591530 | 3 |
| #10588924 | 3 |