Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
492 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 221 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. #41×Dic67 | C2 | semidirect |
| 2. #16863508 | C2 | semidirect |
| 3. #16863503 | C2 | semidirect |
| 4. #16863497 | C2 | semidirect |
| 5. #16863434 | C2 | semidirect |
| 6. #16863392 | C2 | semidirect |
| 7. C2×#14523953 | C2 | semidirect |
| 24. #135×C67 | C4 | semidirect |
| 42. #41×C67 | C2×C4 | semidirect |
| 48. Q16×C67 | C2×C4 | semidirect |
| 49. SD16×C67 | C2×C4 | semidirect |
| 50. D8×C67 | C2×C4 | semidirect |
| 51. C2×C8×C67 | C2×C4 | semidirect |
| 90. C67 | #2943 | semidirect |
| 100. #135 | Dic67 | semidirect |
| 120. #41 | C2×Dic67 | semidirect |
| 128. Q16 | C2×Dic67 | semidirect |
| 129. SD16 | C2×Dic67 | semidirect |
| 130. D8 | C2×Dic67 | semidirect |
| 133. C2×C8 | C2×Dic67 | semidirect |