Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
612 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 612 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. C2×#14523967 | C2 | semidirect |
| 2. C2×#14523964 | C2 | semidirect |
| 3. C2×C22⋊(C67⋊C8) | C2 | semidirect |
| 4. #16863256 | C2 | semidirect |
| 16. C2×#41×C67 | C4 | semidirect |
| 66. Q8×C67 | C22⋊C4 | semidirect |
| 70. D4×C67 | C22⋊C4 | semidirect |
| 116. C67 | #1788 | semidirect |
| 125. C2×#41 | Dic67 | semidirect |
| 182. Q8 | C22⋊Dic67 | semidirect |
| 186. D4 | C22⋊Dic67 | semidirect |