Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 374 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 |
|---|---|---|
| 1. Q8×D268 | C2 | semidirect |
| 2. #16863806 | C2 | semidirect |
| 3. #16863792 | C2 | semidirect |
| 4. #16863693 | C2 | semidirect |
| 5. #16863686 | C2 | semidirect |
| 6. #16863683 | C2 | semidirect |
| 7. #16863676 | C2 | semidirect |
| 8. #16863527 | C2 | semidirect |
| 11. #554×C67 | C2 | semidirect |
| 47. #11761613 | Q8 | semidirect |
| 78. D4×C67 | C2×Q8 | semidirect |
| 98. C67⋊C8 | C2×Q8 | semidirect |
| 122. C67 | #3384 | semidirect |
| 123. #554 | D67 | semidirect |
| 204. D4 | Q8×D67 | semidirect |