Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
162 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 59 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. Q16×Dic83 | C2 | semidirect |
| 4. #19127528 | C2 | semidirect |
| 6. C16×Dic83 | C2 | semidirect |
| 7. #358×C83 | C2 | semidirect |
| 11. #14581735 | C4 | semidirect |
| 30. C83⋊C16 | C2×C4 | semidirect |
| 33. Q16×C83 | C2×C4 | semidirect |
| 62. Dic83 | SD32 | semidirect |
| 68. C83 | C4×SD32 | semidirect |
| 73. #358 | D83 | semidirect |
| 92. Q16 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581735 | 2 |
| Q16×Dic83 | 2 |
| #19127783 | 2 |
| #19127528 | 2 |
| #19127503 | 2 |
| C16×Dic83 | 2 |
| #358×C83 | 2 |
| C4×SD32 | 83 |