Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
332 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 85 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. #41×Dic83 | C2 | semidirect |
| 3. C2×#14581718 | C2 | semidirect |
| 4. #19127674 | C2 | semidirect |
| 5. #19127472 | C2 | semidirect |
| 6. #19127460 | C2 | semidirect |
| 7. #421×C83 | C2 | semidirect |
| 10. #14581822 | C4 | semidirect |
| 12. #14581817 | C4 | semidirect |
| 33. C2×Dic166 | C2×C4 | semidirect |
| 34. C2×D332 | C2×C4 | semidirect |
| 44. #13050574 | C2×C4 | semidirect |
| 130. C83 | #1906 | semidirect |
| 133. #421 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128499 | 2 |
| #41×Dic83 | 2 |
| C2×#14581718 | 2 |
| #19127674 | 2 |
| #19127472 | 2 |
| #19127460 | 2 |
| #421×C83 | 2 |
| #1906 | 83 |