Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
144 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 1. C2×#14523988 | C2 | semidirect |
| 2. #16863671 | C2 | semidirect |
| 4. #16863226 | C2 | semidirect |
| 5. #16863213 | C2 | semidirect |
| 6. #16863210 | C2 | semidirect |
| 7. #504×C67 | C2 | semidirect |
| 72. C67 | #2223 | semidirect |
| 74. #504 | D67 | semidirect |