Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
180 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 77 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. C8×Dic166 | C2 | semidirect |
| 4. #19127452 | C2 | semidirect |
| 5. #19127433 | C2 | semidirect |
| 7. C82×C83 | C2 | semidirect |
| 26. #13050579 | C8 | direct (N × H) |
| 53. Dic166 | C2×C8 | semidirect |
| 57. C8×C83 | C2×C8 | semidirect |
| 58. C8×C83 | SD16 | semidirect |
| 78. C83 | C8×SD16 | semidirect |
| 85. C82 | D83 | semidirect |
| 137. C8 | C8×D83 | semidirect |
| 138. C8 | #13050579 | direct (N × H) |