Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1876 conjugacy classes of subgroups; only the 461 normal subgroups are shown.
This group has 1876 conjugacy classes of subgroups — too many to draw. Only its 461 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. C33×#121 | C2 | semidirect |
| 2. C2×#88860 | C2 | semidirect |
| 3. #11723971 | C2 | semidirect |
| 4. C22×C3⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 5. #11722202 | C2 | semidirect |
| 6. #11722179 | C2 | semidirect |
| 7. #11722177 | C2 | semidirect |
| 22. C32×#121 | D3 | semidirect |
| 45. C3⋊(C3⋊(C3⋊C8)) | D4 | semidirect |
| 65. C22×C33 | D8 | semidirect |
| 75. C3×#121 | C3⋊D3 | semidirect |
| 124. C22×C32 | #213 | semidirect |
| 137. #121 | C3⋊(C3⋊D3) | semidirect |
| 141. C33 | #466 | semidirect |
| 183. C22×C3 | #3753 | semidirect |
| 193. C32 | #5038 | semidirect |
| 225. C22 | #88860 | semidirect |
| 232. C3 | #10592737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#121 | 2 |
| C2×#88860 | 2 |
| #11723971 | 2 |
| C22×C3⋊(C3⋊(C3⋊C8)) | 2 |
| #11722202 | 2 |
| #11722179 | 2 |
| #11722177 | 2 |
| #10592737 | 3 |