Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
144 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 45 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. #16863812 | C2 | semidirect |
| 3. #16863672 | C2 | semidirect |
| 5. #16863211 | C2 | semidirect |
| 6. #16863208 | C2 | semidirect |
| 7. #368×C67 | C2 | semidirect |
| 72. C67 | #2223 | semidirect |
| 77. #368 | D67 | semidirect |