Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 3. C2×#14581790 | C2 | semidirect |
| 5. #19127905 | C2 | direct (N × H) |
| 6. C2×Dic83⋊C8 | C2 | semidirect |
| 7. C2×#14581715 | C2 | semidirect |
| 8. C2×#103×C83 | C2 | semidirect |
| 18. #14581790 | C22 | semidirect |
| 25. Dic83⋊C8 | C22 | semidirect |
| 26. #14581715 | C22 | semidirect |
| 30. #103×C83 | C22 | semidirect |
| 84. C2×Dic83 | SD16 | semidirect |
| 111. Dic83 | C2×SD16 | semidirect |
| 112. C2×C83 | #461 | semidirect |
| 118. C83 | C2×#461 | semidirect |
| 126. C2×#103 | D83 | semidirect |
| 148. #103 | C2×D83 | semidirect |
| 231. C2 | #19127905 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13050579 | 2 |
| C22×#13050577 | 2 |
| C2×#14581790 | 2 |
| C2×#14581754 | 2 |
| #19127905 | 2 |
| C2×Dic83⋊C8 | 2 |
| C2×#14581715 | 2 |
| C2×#103×C83 | 2 |
| C2×#461 | 83 |