Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
596 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 177 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. #19127601 | C2 | semidirect |
| 3. #19127590 | C2 | semidirect |
| 4. #19127586 | C2 | semidirect |
| 5. #19127579 | C2 | semidirect |
| 6. #19127577 | C2 | semidirect |
| 7. C4×C22⋊Dic83 | C2 | semidirect |
| 8. #19127548 | C2 | semidirect |
| 9. #381×C83 | C2 | semidirect |
| 13. #14581766 | C4 | semidirect |
| 38. C2×C22⋊D83 | C2×C4 | semidirect |
| 45. C4⋊Dic83 | C2×C4 | semidirect |
| 51. (C2×D83)⋊C4 | C2×C4 | semidirect |
| 58. C22×C4×C83 | C2×C4 | semidirect |
| 135. C83 | #2333 | semidirect |
| 142. #381 | D83 | semidirect |
| 183. C22×C4 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581766 | 2 |
| #19127601 | 2 |
| #19127590 | 2 |
| #19127586 | 2 |
| #19127579 | 2 |
| #19127577 | 2 |
| C4×C22⋊Dic83 | 2 |
| #19127548 | 2 |
| #381×C83 | 2 |
| #2333 | 83 |