Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1328 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 1328 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 |
|---|---|---|
| 2. C2×C3×#3754 | C2 | semidirect |
| 3. #11723425 | C2 | semidirect |
| 4. C2×#88792 | C2 | semidirect |
| 5. #11722202 | C2 | semidirect |
| 6. #11722032 | C2 | semidirect |
| 7. (C2×D3)⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 12. C2×C3×#634 | C22 | semidirect |
| 18. C4⋊(C3⋊(C3⋊Dic3)) | C22 | semidirect |
| 19. C2×C3⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 21. C2×C3×C3⋊(C3⋊C8) | C22 | semidirect |
| 28. C2×#3754 | D3 | semidirect |
| 73. C2×#634 | C2×D3 | semidirect |
| 90. C2×C3⋊(C3⋊C8) | C2×D3 | semidirect |
| 106. C2×C32×D3 | SD16 | semidirect |
| 240. C2×C3×D3 | #214 | semidirect |
| 261. C33 | #450 | semidirect |
| 366. C2×D3 | #3754 | semidirect |
| 381. C32 | #5169 | semidirect |
| 382. C32 | #5218 | semidirect |
| 437. C3 | #10591458 | semidirect |
| 438. C3 | #10592917 | 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×#3754 | 2 |
| #11723425 | 2 |
| C2×#88792 | 2 |
| #11722202 | 2 |
| #11722032 | 2 |
| (C2×D3)⋊(C3⋊(C3⋊C8)) | 2 |
| #10592917 | 3 |
| #10591458 | 3 |