Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #19128332 | C2 | semidirect |
| 3. #19128006 | C2 | semidirect |
| 4. #19128003 | C2 | semidirect |
| 5. #19127994 | C2 | semidirect |
| 6. #19127979 | C2 | semidirect |
| 7. #19127743 | C2 | semidirect |
| 8. C2×#14581725 | C2 | semidirect |
| 9. #19127729 | C2 | semidirect |
| 64. #41×C83 | Q8 | semidirect |
| 124. C83 | #3083 | semidirect |
| 166. #41 | Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128332 | 2 |
| #19128184 | 2 |
| #19128006 | 2 |
| #19128003 | 2 |
| #19127994 | 2 |
| #19127979 | 2 |
| #19127743 | 2 |
| C2×#14581725 | 2 |
| #19127729 | 2 |
| #19127697 | 2 |
| #417×C83 | 2 |
| #3083 | 83 |