Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #19128426 | C2 | semidirect |
| 3. #19128072 | C2 | semidirect |
| 4. #19127904 | C2 | semidirect |
| 5. #19127903 | C2 | semidirect |
| 6. #19127899 | C2 | semidirect |
| 7. #19127898 | C2 | semidirect |
| 8. C8×Dic166 | C2 | semidirect |
| 9. C4×#13050579 | C2 | semidirect |
| 10. SD16×Dic83 | C2 | semidirect |
| 11. #492×C83 | C2 | semidirect |
| 102. Dic166 | SD16 | semidirect |
| 104. C8×C83 | #41 | semidirect |
| 129. C83 | #3392 | semidirect |
| 133. #492 | D83 | semidirect |
| 234. C8 | #13050589 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128426 | 2 |
| #19128371 | 2 |
| #19128072 | 2 |
| #19127904 | 2 |
| #19127903 | 2 |
| #19127899 | 2 |
| #19127898 | 2 |
| C8×Dic166 | 2 |
| C4×#13050579 | 2 |
| SD16×Dic83 | 2 |
| #492×C83 | 2 |
| #3392 | 83 |