Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
390 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. C2×#14523967 | C2 | semidirect |
| 5. #16863303 | C2 | semidirect |
| 6. #16863150 | C2 | semidirect |
| 7. C22×Q16×C67 | C2 | semidirect |
| 126. C67 | #2015 | semidirect |
| 127. C22×Q16 | D67 | semidirect |