Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
302 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 83 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. #19127744 | C2 | semidirect |
| 5. #19127571 | C2 | semidirect |
| 6. #19127469 | C2 | semidirect |
| 7. #339×C83 | C2 | semidirect |
| 20. #14581720 | C4 | semidirect |
| 38. #13050574 | C2×C4 | semidirect |
| 58. C42×C83 | C2×C4 | semidirect |
| 80. D332 | C4⋊C4 | semidirect |
| 85. Dic166 | C4⋊C4 | semidirect |
| 113. C83 | #1859 | semidirect |
| 120. #339 | D83 | semidirect |
| 171. C42 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128181 | 2 |
| #19127744 | 2 |
| C2×#14581720 | 2 |
| #19127703 | 2 |
| #19127571 | 2 |
| #19127469 | 2 |
| #339×C83 | 2 |
| #1859 | 83 |