Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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. #19128329 | C2 | semidirect |
| 3. #19128011 | C2 | semidirect |
| 4. #19128000 | C2 | semidirect |
| 5. #19127995 | C2 | semidirect |
| 6. #19127980 | C2 | semidirect |
| 7. C2×#14581725 | C2 | semidirect |
| 8. #19127729 | C2 | semidirect |
| 11. #428×C83 | C2 | semidirect |
| 42. #13050590 | Q8 | semidirect |
| 124. C83 | #3083 | semidirect |
| 131. #428 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128329 | 2 |
| #19128182 | 2 |
| #19128011 | 2 |
| #19128000 | 2 |
| #19127995 | 2 |
| #19127980 | 2 |
| C2×#14581725 | 2 |
| #19127729 | 2 |
| #19127703 | 2 |
| #19127695 | 2 |
| #428×C83 | 2 |
| #3083 | 83 |