Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 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. C22×#13050579 | C2 | semidirect |
| 2. #19128272 | C2 | semidirect |
| 4. #19127947 | C2 | semidirect |
| 5. #19127930 | C2 | semidirect |
| 6. #19127739 | C2 | semidirect |
| 7. #19127711 | C2 | semidirect |
| 8. #19127707 | C2 | semidirect |
| 9. C2×#131×C83 | C2 | semidirect |
| 20. #14581771 | C22 | semidirect |
| 25. #14581726 | C22 | semidirect |
| 26. #14581724 | C22 | semidirect |
| 27. #14581717 | C22 | semidirect |
| 32. C2×M16×C83 | C22 | semidirect |
| 34. C22×C8×C83 | C22 | semidirect |
| 67. C2×C8×C83 | D4 | semidirect |
| 121. C83 | #3057 | semidirect |
| 123. C2×#131 | D83 | semidirect |
| 139. C2×M16 | C2×D83 | semidirect |
| 141. C22×C8 | C2×D83 | semidirect |
| 179. C2×C8 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13050579 | 2 |
| #19128272 | 2 |
| #19128265 | 2 |
| #19127947 | 2 |
| #19127930 | 2 |
| #19127739 | 2 |
| #19127711 | 2 |
| #19127707 | 2 |
| C2×#131×C83 | 2 |
| #3057 | 83 |