Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. #16863806 | C2 | semidirect |
| 3. #16863799 | C2 | semidirect |
| 5. #16863691 | C2 | semidirect |
| 6. #16863681 | C2 | semidirect |
| 8. #16863527 | C2 | semidirect |
| 11. #557×C67 | C2 | semidirect |
| 47. #11761615 | Q8 | semidirect |
| 77. Q8×C67 | C2×Q8 | semidirect |
| 96. C67⋊C8 | C2×Q8 | semidirect |
| 117. C67 | #3386 | semidirect |
| 118. #557 | D67 | semidirect |
| 196. Q8 | Q8×D67 | semidirect |