Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
220 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 2. C2×#14523989 | C2 | semidirect |
| 3. C2×#14523988 | C2 | semidirect |
| 4. #16863638 | C2 | semidirect |
| 5. #16863196 | C2 | semidirect |
| 6. (C2×D67)⋊C16 | C2 | semidirect |
| 7. #358×C67 | C2 | semidirect |
| 86. C67 | #2189 | semidirect |
| 91. #358 | D67 | semidirect |