Finite Group DatabasebetaFinite Group DatabasebetaOrder 10688.
322 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 127 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. C22×Dic334 | C2 | semidirect |
| 3. #19128810 | C2 | direct (N × H) |
| 4. C2×Dic167⋊C4 | C2 | semidirect |
| 5. C2×Dic167⋊C4 | C2 | semidirect |
| 8. C2×C4⋊C4×C167 | C2 | semidirect |
| 11. C2×Dic334 | C22 | semidirect |
| 17. Dic167⋊C4 | C22 | semidirect |
| 18. Dic167⋊C4 | C22 | semidirect |
| 24. C4⋊C4×C167 | C22 | semidirect |
| 27. C22×D167 | Q8 | semidirect |
| 51. C2×D167 | C2×Q8 | semidirect |
| 58. C2×C167 | C22⋊Q8 | semidirect |
| 63. C167 | C2×C22⋊Q8 | semidirect |
| 70. C2×C4⋊C4 | D167 | semidirect |
| 86. C4⋊C4 | C2×D167 | semidirect |
| 123. C2 | #19128810 | direct (N × H) |