Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
704 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 161 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. C2×#14581781 | C2 | semidirect |
| 3. C2×D4×Dic83 | C2 | semidirect |
| 4. #19127616 | C2 | semidirect |
| 5. #19127608 | C2 | semidirect |
| 6. #19127603 | C2 | semidirect |
| 7. #19127578 | C2 | semidirect |
| 8. C4×Dic83⋊C4 | C2 | semidirect |
| 9. C2×#124×C83 | C2 | semidirect |
| 51. C4×Dic83 | D4 | semidirect |
| 128. C83 | #2544 | semidirect |
| 131. C2×#124 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581788 | 2 |
| C2×#14581781 | 2 |
| C2×D4×Dic83 | 2 |
| #19127616 | 2 |
| #19127608 | 2 |
| #19127603 | 2 |
| #19127578 | 2 |
| C4×Dic83⋊C4 | 2 |
| C2×#124×C83 | 2 |
| #2544 | 83 |