Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. #19128053 | C2 | semidirect |
| 3. #19128031 | C2 | semidirect |
| 4. #19127988 | C2 | semidirect |
| 5. #19127957 | C2 | semidirect |
| 6. #19127911 | C2 | semidirect |
| 7. #19127861 | C2 | semidirect |
| 8. C4×#13050577 | C2 | semidirect |
| 9. #19127779 | C2 | semidirect |
| 10. #19127700 | C2 | semidirect |
| 11. #554×C83 | C2 | semidirect |
| 127. C83 | #3331 | semidirect |
| 128. #554 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128356 | 2 |
| #19128053 | 2 |
| #19128031 | 2 |
| #19127988 | 2 |
| #19127957 | 2 |
| #19127911 | 2 |
| #19127861 | 2 |
| C4×#13050577 | 2 |
| #19127779 | 2 |
| #19127700 | 2 |
| #554×C83 | 2 |
| #3331 | 83 |