Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. M16×Dic71 | C2 | semidirect |
| 4. C42×Dic71 | C2 | semidirect |
| 5. #17985760 | C2 | semidirect |
| 6. #17985759 | C2 | semidirect |
| 9. Q8×Dic71 | C4 | semidirect |
| 11. D4×Dic71 | C4 | semidirect |
| 18. #14556055 | C4 | semidirect |
| 24. #104×C71 | C4 | semidirect |
| 29. #11765849 | C2×C4 | semidirect |
| 40. C4×Dic71 | C2×C4 | semidirect |
| 54. M16×C71 | C2×C4 | semidirect |
| 57. C42×C71 | C2×C4 | semidirect |
| 61. Q8×C71 | C42 | semidirect |
| 65. D4×C71 | C42 | semidirect |
| 101. Dic71 | #104 | direct (N × H) |
| 108. C71 | C4×#104 | semidirect |
| 130. #104 | Dic71 | direct (N × H) |
| 149. M16 | C2×Dic71 | semidirect |
| 165. C42 | C2×Dic71 | semidirect |
| 169. Q8 | C4×Dic71 | semidirect |
| 173. D4 | C4×Dic71 | semidirect |