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×#14550491 | C2 | semidirect |
| 7. #72221834 | C2 | direct (N × H) |
| 8. #14550491 | C22 | semidirect |
| 16. C2×C3×#6875 | D3 | semidirect |
| 33. C2×#92183 | C9 | semidirect |
| 36. C3×#6875 | C2×D3 | semidirect |
| 74. C2×#6873 | C2×C9 | semidirect |
| 77. #92183 | C2×C9 | semidirect |
| 116. #6873 | C22×C9 | semidirect |
| 164. C2×C3×C27 | D3×C9 | semidirect |
| 232. C3×C27 | C2×D3×C9 | semidirect |
| 420. C2 | #72221834 | 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×#13090955 | 3 |
| C2×#14550491 | 2 |
| C2×D3×#6875 | 3 |
| #72221834 | 2 |