Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
552 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 185 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 |
|---|---|---|
| 3. #19127589 | C2 | semidirect |
| 4. #19127589 | C2 | semidirect |
| 5. #19127588 | C2 | semidirect |
| 6. #19127552 | C2 | semidirect |
| 7. C22⋊C4×Dic83 | C2 | semidirect |
| 8. C4×C22⋊Dic83 | C2 | semidirect |
| 11. #14581773 | C4 | semidirect |
| 34. C22×Dic83 | C2×C4 | semidirect |
| 41. Dic83⋊C4 | C2×C4 | semidirect |
| 45. C22⋊Dic83 | C2×C4 | semidirect |
| 127. C83 | #2374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581773 | 2 |
| #19127604 | 2 |
| #19127589 | 2 |
| #19127588 | 2 |
| #19127552 | 2 |
| C22⋊C4×Dic83 | 2 |
| C4×C22⋊Dic83 | 2 |
| #386×C83 | 2 |
| #2374 | 83 |