Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
360 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 360 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. #19128423 | C2 | semidirect |
| 4. #19128079 | C2 | semidirect |
| 5. #19127926 | C2 | semidirect |
| 6. #19127923 | C2 | semidirect |
| 7. #19127905 | C2 | semidirect |
| 8. C8×Dic166 | C2 | semidirect |
| 9. #19127795 | C2 | semidirect |
| 11. C4×Q16×C83 | C2 | semidirect |
| 115. C83 | #3393 | semidirect |
| 125. C4×Q16 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128423 | 2 |
| #19128086 | 2 |
| #19128085 | 2 |
| #19128079 | 2 |
| #19127926 | 2 |
| #19127923 | 2 |
| #19127905 | 2 |
| C8×Dic166 | 2 |
| #19127795 | 2 |
| #19127783 | 2 |
| C4×Q16×C83 | 2 |
| #3393 | 83 |