Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 1. C22×#13050580 | C2 | semidirect |
| 5. #19127958 | C2 | direct (N × H) |
| 6. C2×#14581723 | C2 | semidirect |
| 7. C2×#14581717 | C2 | semidirect |
| 8. C2×#103×C83 | C2 | semidirect |
| 12. C2×#13050580 | C22 | semidirect |
| 25. #14581723 | C22 | semidirect |
| 26. #14581717 | C22 | semidirect |
| 30. #103×C83 | C22 | semidirect |
| 110. C2×C83 | #470 | semidirect |
| 116. C83 | C2×#470 | semidirect |
| 124. C2×#103 | D83 | semidirect |
| 146. #103 | C2×D83 | semidirect |
| 227. C2 | #19127958 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13050580 | 2 |
| C22×#13050573 | 2 |
| C2×#14581772 | 2 |
| C2×#14581768 | 2 |
| #19127958 | 2 |
| C2×#14581723 | 2 |
| C2×#14581717 | 2 |
| C2×#103×C83 | 2 |
| C2×#470 | 83 |