Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
220 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 2. C2×#14581731 | C2 | semidirect |
| 3. #108×D83 | C2 | semidirect |
| 4. #19127509 | C2 | semidirect |
| 5. #19127508 | C2 | semidirect |
| 6. #19127507 | C2 | semidirect |
| 7. #359×C83 | C2 | semidirect |
| 21. C2×C83⋊C16 | C22 | semidirect |
| 22. #14581728 | C22 | semidirect |
| 25. C2×C16×C83 | C22 | semidirect |
| 26. #108×C83 | C22 | semidirect |
| 109. C83 | #2143 | semidirect |
| 116. #359 | D83 | semidirect |
| 132. C2×C16 | C2×D83 | semidirect |
| 135. #108 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×D83 | 2 |
| C2×#14581731 | 2 |
| #108×D83 | 2 |
| #19127509 | 2 |
| #19127508 | 2 |
| #19127507 | 2 |
| #359×C83 | 2 |
| #2143 | 83 |