Finite Group DatabasebetaFinite Group DatabasebetaOrder 2916.
552 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 87 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. #13090650 | C2 | direct (N × H) |
| 2. C2×#10624558 | C2 | semidirect |
| 5. C2×#92158 | C3 | semidirect |
| 6. C2×#92158 | C3 | semidirect |
| 7. #10624558 | C22 | semidirect |
| 15. C2×#6855 | C2×C3 | semidirect |
| 16. C2×#6855 | C2×C3 | semidirect |
| 17. #92158 | C2×C3 | semidirect |
| 18. #92158 | C2×C3 | semidirect |
| 34. #6855 | C22×C3 | semidirect |
| 35. #6855 | C22×C3 | semidirect |
| 47. C2×C3×3−1+2 | D9 | semidirect |
| 77. C2×C3⋊D9 | 3−1+2 | semidirect |
| 98. C3×3−1+2 | C2×D9 | semidirect |
| 171. C2×C3×C9 | C3×D9 | semidirect |
| 172. C2×C3×C9 | C3×D9 | semidirect |
| 173. C2×C3×C9 | C2×3−1+2 | semidirect |
| 174. C3⋊D9 | C2×3−1+2 | semidirect |
| 250. C3×C9 | C2×C3×D9 | semidirect |
| 251. C3×C9 | C2×C3×D9 | semidirect |
| 252. C3×C9 | C22×3−1+2 | semidirect |
| 386. C2 | #13090650 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13090650 | 2 |
| C2×#10624558 | 2 |
| C2×C3⋊D3×3−1+2 | 3 |
| C2×C32×C3⋊D9 | 3 |
| C2×#92158 | 3 |