Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1388 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 1388 conjugacy classes of subgroups — too many to draw. Only its 200 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×C32×D3×D4 | C2 | semidirect |
| 2. C2×C3×#3753 | C2 | semidirect |
| 3. #11723515 | C2 | semidirect |
| 4. C2×#88789 | C2 | semidirect |
| 5. #11722202 | C2 | semidirect |
| 6. #11722032 | C2 | semidirect |
| 7. (C2×D3)⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 12. C2×C3×C4⋊(C3⋊D3) | C22 | semidirect |
| 19. C4⋊(C3⋊(C3⋊Dic3)) | C22 | semidirect |
| 20. C2×C3⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 22. C2×C3×C3⋊(C3⋊C8) | C22 | semidirect |
| 26. C2×C3×D3×D4 | D3 | semidirect |
| 28. C2×#3753 | D3 | semidirect |
| 48. C33×D4 | D4 | semidirect |
| 56. C32×D12 | D4 | semidirect |
| 75. C2×C4⋊(C3⋊D3) | C2×D3 | semidirect |
| 92. C2×C3⋊(C3⋊C8) | C2×D3 | semidirect |
| 110. C2×C32×D3 | D8 | semidirect |
| 116. C2×D3×D4 | C3⋊D3 | semidirect |
| 152. C32×D4 | #67 | semidirect |
| 153. C32×D4 | #67 | semidirect |
| 171. C3×D12 | #67 | semidirect |
| 252. C2×C3×D3 | #213 | semidirect |
| 271. C33 | #447 | semidirect |
| 296. C3×D4 | #625 | semidirect |
| 297. C3×D4 | #638 | semidirect |
| 314. D12 | #638 | semidirect |
| 386. C2×D3 | #3753 | semidirect |
| 399. C32 | #5156 | semidirect |
| 400. C32 | #5217 | semidirect |
| 415. D4 | #6290 | semidirect |
| 460. C3 | #10591447 | semidirect |
| 461. C3 | #10592916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D3×D4 | 2 |
| C2×C3×#3753 | 2 |
| #11723515 | 2 |
| C2×#88789 | 2 |
| #11722202 | 2 |
| #11722032 | 2 |
| (C2×D3)⋊(C3⋊(C3⋊C8)) | 2 |
| #10592916 | 3 |
| #10591447 | 3 |