Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1708 conjugacy classes of subgroups; only the 685 normal subgroups are shown.
This group has 1708 conjugacy classes of subgroups — too many to draw. Only its 685 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×#88855 | C2 | semidirect |
| 3. #11722200 | C2 | semidirect |
| 4. C4⋊(C3⋊(C3⋊(C3⋊C8))) | C2 | semidirect |
| 5. C4×C3⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 31. C3⋊(C3⋊(C3⋊C8)) | D4 | semidirect |
| 48. C33×C4 | M16 | semidirect |
| 87. C32×C4 | #208 | semidirect |
| 95. C33 | #436 | semidirect |
| 126. C3×C4 | #3748 | semidirect |
| 129. C32 | #5012 | semidirect |
| 151. C4 | #88855 | semidirect |
| 154. C3 | #10592711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4×D4 | 2 |
| C2×#88855 | 2 |
| #11722200 | 2 |
| C4⋊(C3⋊(C3⋊(C3⋊C8))) | 2 |
| C4×C3⋊(C3⋊(C3⋊C8)) | 2 |
| #10592711 | 3 |