Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
532 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#14581824 | C2 | semidirect |
| 3. C2×Q16×D83 | C2 | semidirect |
| 4. #19128276 | C2 | semidirect |
| 5. #19128094 | C2 | semidirect |
| 6. #19128093 | C2 | semidirect |
| 7. #19128086 | C2 | semidirect |
| 8. #19128085 | C2 | semidirect |
| 9. #19128079 | C2 | semidirect |
| 10. #19127655 | C2 | semidirect |
| 11. #494×C83 | C2 | semidirect |
| 122. C83 | #3156 | semidirect |
| 132. #494 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581824 | 2 |
| C2×#14581815 | 2 |
| C2×Q16×D83 | 2 |
| #19128276 | 2 |
| #19128094 | 2 |
| #19128093 | 2 |
| #19128086 | 2 |
| #19128085 | 2 |
| #19128079 | 2 |
| #19127655 | 2 |
| #494×C83 | 2 |
| #3156 | 83 |