Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
596 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×C4⋊Dic83 | C2 | semidirect |
| 3. #19127628 | C2 | semidirect |
| 4. #19127603 | C2 | semidirect |
| 5. #19127578 | C2 | semidirect |
| 6. #19127567 | C2 | semidirect |
| 7. C4×C22⋊C4×C83 | C2 | semidirect |
| 93. C83 | #2504 | semidirect |
| 100. C4×C22⋊C4 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581766 | 2 |
| C22×C4⋊Dic83 | 2 |
| #19127628 | 2 |
| #19127603 | 2 |
| #19127578 | 2 |
| #19127567 | 2 |
| C4×C22⋊C4×C83 | 2 |
| #2504 | 83 |