Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
174 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 174 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×#14523984 | C2 | semidirect |
| 2. C2×C16×D67 | C2 | semidirect |
| 3. #16863633 | C2 | semidirect |
| 4. #16863629 | C2 | semidirect |
| 5. #16863221 | C2 | semidirect |
| 6. #16863198 | C2 | semidirect |
| 7. #357×C67 | C2 | semidirect |
| 33. C67⋊C16 | D4 | semidirect |
| 67. C2×D67 | D16 | semidirect |
| 80. C67 | #2215 | semidirect |
| 87. #357 | D67 | semidirect |