Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
404 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 141 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. #16864125 | C2 | semidirect |
| 3. #16863769 | C2 | semidirect |
| 4. #16863602 | C2 | semidirect |
| 5. #16863597 | C2 | semidirect |
| 6. C4×#11761617 | C2 | semidirect |
| 7. C8×Q8×C67 | C2 | semidirect |
| 45. Q8×C67 | SD16 | semidirect |
| 60. C8×C67 | #41 | semidirect |
| 77. C67 | #3392 | semidirect |
| 83. C8×Q8 | D67 | semidirect |
| 124. Q8 | #11761617 | semidirect |
| 137. C8 | #11761629 | semidirect |