Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
408 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 119 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. #19128252 | C2 | semidirect |
| 2. #19128236 | C2 | semidirect |
| 3. #19128090 | C2 | semidirect |
| 4. #19128067 | C2 | semidirect |
| 5. #19128063 | C2 | semidirect |
| 6. #19127955 | C2 | semidirect |
| 7. #19127948 | C2 | semidirect |
| 8. #19127788 | C2 | semidirect |
| 9. #19127783 | C2 | semidirect |
| 10. #19127653 | C2 | semidirect |
| 11. #501×C83 | C2 | semidirect |
| 109. C8×C83 | #41 | semidirect |
| 138. C83 | #3171 | semidirect |
| 141. #501 | D83 | semidirect |
| 248. C8 | #13050591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128252 | 2 |
| #19128236 | 2 |
| #19128090 | 2 |
| #19128067 | 2 |
| #19128063 | 2 |
| #19127955 | 2 |
| #19127948 | 2 |
| #19127788 | 2 |
| #19127783 | 2 |
| #19127653 | 2 |
| #501×C83 | 2 |
| #3171 | 83 |