Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 460 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. #16864068 | C2 | semidirect |
| 2. #16863773 | C2 | semidirect |
| 3. #16863592 | C2 | semidirect |
| 4. C4×D536 | C2 | semidirect |
| 5. C8×Q8×C67 | C2 | semidirect |
| 32. Q8×C67 | D8 | semidirect |
| 43. C8×C67 | #41 | semidirect |
| 58. C67 | #3391 | semidirect |
| 62. C8×Q8 | D67 | semidirect |
| 90. Q8 | D536 | semidirect |
| 101. C8 | #11761629 | semidirect |