Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
644 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×C3×D4×D9 | C2 | semidirect |
| 2. C2×C9×#213 | C2 | semidirect |
| 3. #11721036 | C2 | semidirect |
| 4. C2×#88421 | C2 | semidirect |
| 5. #11720576 | C2 | semidirect |
| 6. #11720283 | C2 | semidirect |
| 7. (C2×D9)⋊(C3⋊C8) | C2 | semidirect |
| 15. C2×C9×D12 | C22 | semidirect |
| 19. C4⋊(C3⋊Dic9) | C22 | semidirect |
| 20. C2×C3⋊(C9⋊C8) | C22 | semidirect |
| 22. C2×C9×C3⋊C8 | C22 | semidirect |
| 29. C2×D4×D9 | D3 | semidirect |
| 48. C3×D4×C9 | D4 | semidirect |
| 56. C3×D36 | D4 | semidirect |
| 110. C2×C3×D9 | D8 | semidirect |
| 121. C2×#213 | D9 | semidirect |
| 165. D4×C9 | #67 | semidirect |
| 174. D36 | #67 | semidirect |
| 205. C2×D12 | C2×D9 | semidirect |
| 220. C2×C3⋊C8 | C2×D9 | semidirect |
| 256. C2×D9 | #213 | semidirect |
| 271. C3×C9 | #447 | semidirect |
| 296. C3×D4 | #611 | semidirect |
| 400. C9 | #5217 | semidirect |
| 415. D4 | #6194 | semidirect |
| 460. C3 | #10588836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×D9 | 2 |
| C2×C9×#213 | 2 |
| #11721036 | 2 |
| C2×#88421 | 2 |
| #11720576 | 2 |
| #11720283 | 2 |
| (C2×D9)⋊(C3⋊C8) | 2 |
| #10591447 | 3 |
| #10588836 | 3 |