Finite Group DatabasebetaFinite Group DatabasebetaOrder 2916.
493 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 493 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | #4169 |
| commutator, cosocle, hypocenter | C32⋊C9 | C22×C32 |
| Frattini | C33 | C2×C32×D3 |
| Fitting | C2×#10624688 | C2 |
| socle | C2×C32 | C3×(C3⋊D3)⋊C3 |
| prime radical | C2×#92174 | C3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C2×C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13090904 | C2 | direct (N × H) |
| 2. C2×#10624688 | C2 | semidirect |
| 4. C2×#92295 | C3 | semidirect |
| 5. C2×#92178 | C3 | semidirect |
| 6. C2×#92176 | C3 | semidirect |
| 8. #10624688 | C22 | semidirect |
| 12. C2×#6887 | C2×C3 | semidirect |
| 13. #92295 | C2×C3 | semidirect |
| 15. C2×#6868 | C2×C3 | semidirect |
| 17. C2×#6867 | C2×C3 | semidirect |
| 20. #92178 | C2×C3 | semidirect |
| 21. #92176 | C2×C3 | semidirect |
| 34. #6887 | C22×C3 | semidirect |
| 36. #6868 | C22×C3 | semidirect |
| 38. #6867 | C22×C3 | semidirect |
| 51. C2×C32×C9 | D9 | semidirect |
| 97. C32×C9 | C2×D9 | semidirect |
| 300. C2 | #13090904 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13090904 | 2 |
| C2×#10624688 | 2 |
| C2×C3×C9×C3⋊D3 | 3 |
| C2×#92295 | 3 |
| C2×#92178 | 3 |
| C2×#92176 | 3 |
| C2×#92174 | 3 |