Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 1. C2×#14581825 | C2 | semidirect |
| 3. #19128272 | C2 | semidirect |
| 4. #19128182 | C2 | semidirect |
| 5. #19127922 | C2 | semidirect |
| 6. #19127915 | C2 | semidirect |
| 7. #19127910 | C2 | semidirect |
| 8. #19127905 | C2 | semidirect |
| 9. #19127729 | C2 | semidirect |
| 10. C2×#14581715 | C2 | semidirect |
| 11. #417×C83 | C2 | semidirect |
| 147. C83 | #3046 | semidirect |
| 157. #417 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581825 | 2 |
| C2×#14581812 | 2 |
| #19128272 | 2 |
| #19128182 | 2 |
| #19127922 | 2 |
| #19127915 | 2 |
| #19127910 | 2 |
| #19127905 | 2 |
| #19127729 | 2 |
| C2×#14581715 | 2 |
| #417×C83 | 2 |
| #3046 | 83 |