Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 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. #19128421 | C2 | semidirect |
| 3. #19128081 | C2 | semidirect |
| 4. #19127922 | C2 | semidirect |
| 5. #19127906 | C2 | semidirect |
| 6. C8×Dic166 | C2 | semidirect |
| 7. #19127795 | C2 | semidirect |
| 85. C83 | #3393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128421 | 2 |
| #19128084 | 2 |
| #19128081 | 2 |
| #19127922 | 2 |
| #19127906 | 2 |
| C8×Dic166 | 2 |
| #19127795 | 2 |
| C4×D8×C83 | 2 |
| #3393 | 83 |