Finite Group DatabasebetaFinite Group DatabasebetaOrder 2916.
332 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 84 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. #13090955 | C2 | direct (N × H) |
| 2. C2×#10624704 | C2 | semidirect |
| 5. C2×#92183 | C3 | semidirect |
| 6. C2×#92183 | C3 | semidirect |
| 7. #10624704 | C22 | semidirect |
| 11. C2×C3×C27⋊C3 | D3 | semidirect |
| 15. C2×#6873 | C2×C3 | semidirect |
| 16. C2×#6873 | C2×C3 | semidirect |
| 17. #92183 | C2×C3 | semidirect |
| 18. #92183 | C2×C3 | semidirect |
| 29. C3×C27⋊C3 | C2×D3 | semidirect |
| 32. #6873 | C22×C3 | semidirect |
| 33. #6873 | C22×C3 | semidirect |
| 58. C2×C3×C27 | C3×D3 | semidirect |
| 59. C2×C3×C27 | C3×D3 | semidirect |
| 90. C3×C27 | C2×C3×D3 | semidirect |
| 91. C3×C27 | C2×C3×D3 | semidirect |
| 222. C2 | #13090955 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13090955 | 2 |
| C2×#10624704 | 2 |
| C2×C3×#4208 | 3 |
| C2×D3×C27⋊C3 | 3 |
| C2×#92183 | 3 |