Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 115 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. #19128437 | C2 | semidirect |
| 2. #19128366 | C2 | semidirect |
| 3. #19128059 | C2 | semidirect |
| 4. #19127989 | C2 | semidirect |
| 5. #19127983 | C2 | semidirect |
| 6. #19127915 | C2 | semidirect |
| 8. #19127831 | C2 | semidirect |
| 9. #19127810 | C2 | semidirect |
| 10. C4×#13050579 | C2 | semidirect |
| 11. #486×C83 | C2 | semidirect |
| 125. C83 | #3373 | semidirect |
| 129. #486 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128437 | 2 |
| #19128366 | 2 |
| #19128059 | 2 |
| #19127989 | 2 |
| #19127983 | 2 |
| #19127915 | 2 |
| #19127893 | 2 |
| #19127831 | 2 |
| #19127810 | 2 |
| C4×#13050579 | 2 |
| #486×C83 | 2 |
| #3373 | 83 |