Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
152 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 93 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. #16863219 | C2 | direct (N × H) |
| 12. M32×C67 | C4 | semidirect |
| 14. C2×C16×C67 | C4 | semidirect |
| 28. C16×C67 | C2×C4 | semidirect |
| 54. C2×C67 | #365 | semidirect |
| 57. C67 | C2×#365 | semidirect |
| 65. M32 | Dic67 | semidirect |
| 67. C2×C16 | Dic67 | semidirect |
| 85. C16 | C2×Dic67 | semidirect |
| 111. C2 | #16863219 | direct (N × H) |