Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
5964 conjugacy classes of subgroups; only the 907 normal subgroups are shown.
This group has 5964 conjugacy classes of subgroups — too many to draw. Only its 907 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. C22×#6312 | C2 | semidirect |
| 2. C22×#6312 | C2 | semidirect |
| 3. C22×C4⋊(C3⋊(C3⋊D3)) | C2 | semidirect |
| 4. C22×C4×C3⋊(C3⋊D3) | C2 | semidirect |
| 5. C2×C33×C22⋊C4 | C2 | semidirect |
| 6. C2×#88859 | C2 | semidirect |
| 7. C2×#88857 | C2 | semidirect |
| 8. #11723925 | C2 | direct (N × H) |
| 17. C2×#6312 | C22 | semidirect |
| 18. C2×#6312 | C22 | semidirect |
| 22. C2×C4⋊(C3⋊(C3⋊D3)) | C22 | semidirect |
| 24. C2×C4×C3⋊(C3⋊D3) | C22 | semidirect |
| 25. C33×C22⋊C4 | C22 | semidirect |
| 26. #88859 | C22 | semidirect |
| 27. #88857 | C22 | semidirect |
| 32. C2×C32×C22⋊C4 | D3 | semidirect |
| 46. C22×C3⋊(C3⋊D3) | D4 | semidirect |
| 56. C2×C3⋊(C3⋊Dic3) | D4 | semidirect |
| 77. C32×C22⋊C4 | C2×D3 | semidirect |
| 95. C2×C3⋊(C3⋊D3) | C2×D4 | semidirect |
| 99. C3⋊(C3⋊Dic3) | C2×D4 | semidirect |
| 104. C2×C3×C22⋊C4 | C3⋊D3 | semidirect |
| 135. C2×C33 | #121 | semidirect |
| 156. C3×C22⋊C4 | C2×C3⋊D3 | semidirect |
| 186. C2×C22⋊C4 | C3⋊(C3⋊D3) | semidirect |
| 187. C33 | C2×#121 | semidirect |
| 214. C2×C32 | #884 | semidirect |
| 237. C22⋊C4 | C2×C3⋊(C3⋊D3) | semidirect |
| 258. C32 | C2×#884 | semidirect |
| 285. C2×C3 | #64093 | semidirect |
| 311. C3 | C2×#64093 | semidirect |
| 315. C2 | #11723925 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6312 | 2 |
| C22×C4⋊(C3⋊(C3⋊D3)) | 2 |
| C22×C4×C3⋊(C3⋊D3) | 2 |
| C2×C33×C22⋊C4 | 2 |
| C2×#88859 | 2 |
| C2×#88857 | 2 |
| #11723925 | 2 |
| C2×#64093 | 3 |