Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 1. #19128355 | C2 | semidirect |
| 2. #19128097 | C2 | semidirect |
| 3. #19128025 | C2 | semidirect |
| 4. #19128017 | C2 | semidirect |
| 5. #19127988 | C2 | semidirect |
| 6. #19127981 | C2 | semidirect |
| 7. #19127952 | C2 | semidirect |
| 8. C4×#13050575 | C2 | semidirect |
| 9. #19127779 | C2 | semidirect |
| 10. #19127744 | C2 | semidirect |
| 11. #555×C83 | C2 | semidirect |
| 101. C83⋊C8 | #41 | semidirect |
| 128. C83 | #3354 | semidirect |
| 129. #555 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128355 | 2 |
| #19128097 | 2 |
| #19128025 | 2 |
| #19128017 | 2 |
| #19127988 | 2 |
| #19127981 | 2 |
| #19127952 | 2 |
| C4×#13050575 | 2 |
| #19127779 | 2 |
| #19127744 | 2 |
| #555×C83 | 2 |
| #3354 | 83 |