Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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×#14524069 | C2 | semidirect |
| 2. #16863974 | C2 | semidirect |
| 3. C2×#14523970 | C2 | semidirect |
| 4. C2×#14523969 | C2 | semidirect |
| 5. #16863299 | C2 | semidirect |
| 6. #16863164 | C2 | semidirect |
| 7. C2×AGL(1,ℤ/8)×C67 | C2 | semidirect |
| 45. #11761612 | D4 | semidirect |
| 68. C2×D4×C67 | D4 | semidirect |
| 74. M16×C67 | D4 | semidirect |
| 153. C67 | #2006 | semidirect |
| 155. C2×AGL(1,ℤ/8) | D67 | semidirect |
| 205. C2×D4 | C22⋊D67 | semidirect |
| 218. M16 | C22⋊D67 | semidirect |