Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 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. #16864068 | C2 | semidirect |
| 2. #16863762 | C2 | semidirect |
| 3. #16863744 | C2 | semidirect |
| 4. #16863693 | C2 | semidirect |
| 5. #16863683 | C2 | semidirect |
| 6. #16863591 | C2 | semidirect |
| 7. #16863591 | C2 | semidirect |
| 8. #16863527 | C2 | semidirect |
| 9. #16863506 | C2 | semidirect |
| 10. C4×#11761613 | C2 | semidirect |
| 11. #554×C67 | C2 | semidirect |
| 80. D4×C67 | #41 | semidirect |
| 130. C67 | #3366 | semidirect |
| 131. #554 | D67 | semidirect |
| 218. D4 | #11761629 | semidirect |