Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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. #19128281 | C2 | semidirect |
| 2. #19128035 | C2 | semidirect |
| 3. #19128016 | C2 | semidirect |
| 4. #19127949 | C2 | semidirect |
| 5. #19127937 | C2 | semidirect |
| 6. #19127862 | C2 | semidirect |
| 7. #19127849 | C2 | semidirect |
| 8. #19127667 | C2 | semidirect |
| 9. #467×C83 | C2 | semidirect |
| 120. C83 | #3203 | semidirect |
| 125. #467 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128281 | 2 |
| #19128035 | 2 |
| #19128016 | 2 |
| #19127949 | 2 |
| #19127937 | 2 |
| #19127862 | 2 |
| #19127849 | 2 |
| #19127667 | 2 |
| #467×C83 | 2 |
| #3203 | 83 |