Finite Group DatabasebetaFinite Group DatabasebetaOrder 8748.
598 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 5. C2×#14550493 | C2 | semidirect |
| 7. #72221833 | C2 | direct (N × H) |
| 8. #14550493 | C22 | semidirect |
| 16. C2×C3×#6875 | D3 | semidirect |
| 33. C2×#92181 | C9 | semidirect |
| 36. C3×#6875 | C2×D3 | semidirect |
| 76. C2×#6872 | C2×C9 | semidirect |
| 79. #92181 | C2×C9 | semidirect |
| 122. #6872 | C22×C9 | semidirect |
| 174. C2×C3×C27 | D3×C9 | semidirect |
| 256. C3×C27 | C2×D3×C9 | semidirect |
| 476. C2 | #72221833 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#13091386 | 3 |
| C2×#13090945 | 3 |
| C2×#14550493 | 2 |
| C2×D3×#6875 | 3 |
| #72221833 | 2 |