Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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. #19127959 | C2 | semidirect |
| 5. #19127947 | C2 | semidirect |
| 6. #19127942 | C2 | semidirect |
| 7. #19127930 | C2 | semidirect |
| 8. #19127743 | C2 | semidirect |
| 9. #19127698 | C2 | semidirect |
| 10. C2×#14581717 | C2 | semidirect |
| 11. C2×#131×C83 | C2 | semidirect |
| 79. M16×C83 | D4 | semidirect |
| 144. C83 | #3063 | semidirect |
| 146. C2×#131 | D83 | semidirect |
| 210. M16 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581825 | 2 |
| #19128279 | 2 |
| #19128272 | 2 |
| #19127959 | 2 |
| #19127947 | 2 |
| #19127942 | 2 |
| #19127930 | 2 |
| #19127743 | 2 |
| #19127698 | 2 |
| C2×#14581717 | 2 |
| C2×#131×C83 | 2 |
| #3063 | 83 |