Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. #19128178 | C2 | semidirect |
| 4. #19127798 | C2 | semidirect |
| 5. #19127792 | C2 | semidirect |
| 6. #19127737 | C2 | semidirect |
| 7. #19127711 | C2 | semidirect |
| 8. #19127659 | C2 | semidirect |
| 11. C2×#13050578 | C4 | semidirect |
| 16. #14581757 | C22 | semidirect |
| 23. #14581725 | C22 | semidirect |
| 24. #14581723 | C22 | semidirect |
| 25. #14581717 | C22 | semidirect |
| 26. #14581702 | C22 | semidirect |
| 27. C8×Dic83 | C22 | semidirect |
| 34. C2×Dic166 | C2×C4 | semidirect |
| 38. #13050578 | C2×C4 | semidirect |
| 39. #13050578 | C2×C4 | semidirect |
| 40. C2×C83⋊C8 | C2×C4 | semidirect |
| 104. C83 | #2949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13050578 | 2 |
| #19128178 | 2 |
| #19128176 | 2 |
| #19127798 | 2 |
| #19127792 | 2 |
| #19127737 | 2 |
| #19127711 | 2 |
| #19127659 | 2 |
| #418×C83 | 2 |
| #2949 | 83 |