Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16864131 | C2 | semidirect |
| 2. #16864119 | C2 | semidirect |
| 3. #16863780 | C2 | semidirect |
| 4. #16863769 | C2 | semidirect |
| 5. #16863619 | C2 | semidirect |
| 6. #16863612 | C2 | semidirect |
| 7. #16863607 | C2 | semidirect |
| 9. C4×#11761617 | C2 | semidirect |
| 10. C4×#11761617 | C2 | semidirect |
| 11. C8×Q8×C67 | C2 | semidirect |
| 126. C67 | #3394 | semidirect |
| 135. C8×Q8 | D67 | semidirect |