Finite Group DatabasebetaFinite Group DatabasebetaOrder 2916.
239 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 239 conjugacy classes of subgroups — too many to draw. Only its 63 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. #10624709⋊C2 | C2 | direct (N × H) |
| 2. C2×#10624709 | C2 | semidirect |
| 6. #10624709 | C22 | semidirect |
| 13. C2×#6875 | D3 | semidirect |
| 16. C2×C3⋊D27 | C9 | semidirect |
| 26. #6875 | C2×D3 | semidirect |
| 36. C2×C3×C27 | C2×C9 | semidirect |
| 42. C3⋊D27 | C2×C9 | semidirect |
| 63. C3×C27 | C22×C9 | semidirect |
| 158. C2 | #10624709⋊C2 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624709⋊C2 | 2 |
| C2×#10624709 | 2 |
| C2×C3⋊(D27⋊C3) | 3 |
| C2×#92294 | 3 |
| C2×AGL(1,ℤ/27) | 3 |