Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19128425 | C2 | semidirect |
| 3. #19128082 | C2 | semidirect |
| 4. #19127921 | C2 | semidirect |
| 5. #19127918 | C2 | semidirect |
| 6. #19127908 | C2 | semidirect |
| 8. C8×Dic166 | C2 | semidirect |
| 9. C4×#13050579 | C2 | semidirect |
| 10. SD16×Dic83 | C2 | semidirect |
| 11. #492×C83 | C2 | semidirect |
| 126. C83 | #3394 | semidirect |
| 130. #492 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128437 | 2 |
| #19128425 | 2 |
| #19128082 | 2 |
| #19127921 | 2 |
| #19127918 | 2 |
| #19127908 | 2 |
| #19127893 | 2 |
| C8×Dic166 | 2 |
| C4×#13050579 | 2 |
| SD16×Dic83 | 2 |
| #492×C83 | 2 |
| #3394 | 83 |