Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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. C22×#11761611 | C2 | semidirect |
| 3. C2×#14523965 | C2 | semidirect |
| 4. C2×#14523963 | C2 | semidirect |
| 5. #16863253 | C2 | semidirect |
| 6. #16863158 | C2 | semidirect |
| 7. #340×C67 | C2 | semidirect |
| 16. #14524018 | C4 | semidirect |
| 48. C2×C67⋊C8 | D4 | semidirect |
| 58. C2×C8×C67 | D4 | semidirect |
| 146. C67 | #1895 | semidirect |
| 153. #340 | D67 | semidirect |
| 200. C2×C8 | D268 | semidirect |