Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
872 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 872 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. C3×#64078 | C2 | semidirect |
| 4. C4⋊(C3⋊(C3⋊(C3⋊C8))) | C2 | semidirect |
| 5. #11722039 | C2 | semidirect |
| 20. #64078 | D3 | semidirect |
| 70. C33×C4 | SD16 | semidirect |
| 157. C32×C4 | #214 | semidirect |
| 158. C32×C4 | #215 | semidirect |
| 171. C33 | #461 | semidirect |
| 238. C3×C4 | #3715 | semidirect |
| 239. C3×C4 | #3754 | semidirect |
| 247. C32 | #5019 | semidirect |
| 248. C32 | #5083 | semidirect |
| 279. C4 | #88792 | semidirect |
| 283. C3 | #10590363 | semidirect |
| 284. C3 | #10592718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64078 | 2 |
| C32×C4×D12 | 2 |
| C2×#88792 | 2 |
| C4⋊(C3⋊(C3⋊(C3⋊C8))) | 2 |
| #11722039 | 2 |
| #10592718 | 3 |
| #10590363 | 3 |