Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
138 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 53 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. #16863798 | C2 | semidirect |
| 3. #16863201 | C2 | semidirect |
| 5. C4×C16×C67 | C2 | semidirect |
| 50. C67 | #2242 | semidirect |
| 55. C4×C16 | D67 | semidirect |