Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19128272 | C2 | semidirect |
| 3. #19128043 | C2 | semidirect |
| 4. #19128026 | C2 | semidirect |
| 5. #19127947 | C2 | semidirect |
| 6. #19127930 | C2 | semidirect |
| 7. #19127854 | C2 | semidirect |
| 8. #19127842 | C2 | semidirect |
| 9. #408×C83 | C2 | semidirect |
| 10. C22×Dic166 | C22 | semidirect |
| 21. #14581771 | C22 | semidirect |
| 27. #14581751 | C22 | semidirect |
| 28. #14581726 | C22 | semidirect |
| 29. #14581724 | C22 | semidirect |
| 30. #14581717 | C22 | semidirect |
| 31. #14581717 | C22 | semidirect |
| 35. C2×M16×C83 | C22 | semidirect |
| 36. C22×C8×C83 | C22 | semidirect |
| 38. C22⋊C8×C83 | C22 | semidirect |
| 138. C83 | #3200 | semidirect |
| 147. #408 | D83 | semidirect |
| 153. C2×M16 | C2×D83 | semidirect |
| 154. C22×C8 | C2×D83 | semidirect |
| 176. C22⋊C8 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128272 | 2 |
| #19128265 | 2 |
| #19128043 | 2 |
| #19128026 | 2 |
| #19127947 | 2 |
| #19127930 | 2 |
| #19127854 | 2 |
| #19127842 | 2 |
| #408×C83 | 2 |
| #3200 | 83 |