Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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×#14581718 | C2 | semidirect |
| 3. #19127703 | C2 | semidirect |
| 4. #19127604 | C2 | semidirect |
| 5. C2×#100×C83 | C2 | semidirect |
| 8. #14581837 | C4 | semidirect |
| 13. C2×C4⋊Dic83 | C22 | semidirect |
| 15. C2×C4×Dic83 | C22 | semidirect |
| 20. C2×M16×C83 | C22 | semidirect |
| 80. D332 | C22⋊C4 | semidirect |
| 84. Dic166 | C22⋊C4 | semidirect |
| 113. C83 | #1792 | semidirect |
| 117. C2×#100 | D83 | semidirect |
| 127. C2×M16 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581837 | 2 |
| C2×#14581718 | 2 |
| #19127703 | 2 |
| #19127604 | 2 |
| C2×#100×C83 | 2 |
| #1792 | 83 |