Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #19128042 | C2 | semidirect |
| 3. #19128031 | C2 | semidirect |
| 4. #19128025 | C2 | semidirect |
| 5. #19128019 | C2 | semidirect |
| 6. #19127744 | C2 | semidirect |
| 7. C2×#14581723 | C2 | semidirect |
| 8. #19127700 | C2 | semidirect |
| 9. #19127695 | C2 | semidirect |
| 10. #19127668 | C2 | semidirect |
| 11. #520×C83 | C2 | semidirect |
| 134. C83 | #3099 | semidirect |
| 136. #520 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128279 | 2 |
| #19128042 | 2 |
| #19128031 | 2 |
| #19128025 | 2 |
| #19128019 | 2 |
| #19127744 | 2 |
| C2×#14581723 | 2 |
| #19127700 | 2 |
| #19127695 | 2 |
| #19127668 | 2 |
| #520×C83 | 2 |
| #3099 | 83 |