Finite Group DatabasebetaFinite Group DatabasebetaOrder 8748.
2545 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 2545 conjugacy classes of subgroups — too many to draw. Only its 151 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 |
|---|---|---|
| 6. C2×#14552273 | C2 | semidirect |
| 7. #72221835 | C2 | direct (N × H) |
| 8. #14552273 | C22 | semidirect |
| 16. C2×C32×C9⋊C9 | D3 | semidirect |
| 22. C2×#10624556 | D3 | semidirect |
| 38. C32×C9⋊C9 | C2×D3 | semidirect |
| 44. #10624556 | C2×D3 | semidirect |
| 387. C2×C3×C9 | #4208 | semidirect |
| 478. C3×C9 | C2×#4208 | semidirect |
| 604. C2 | #72221835 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×((C3⋊D3)⋊C9)⋊C9 | 3 |
| C2×C3⋊D3×C9⋊C9 | 3 |
| C2×#13090642 | 3 |
| C2×C3×C3⋊#4208 | 3 |
| C2×#14552273 | 2 |
| #72221835 | 2 |