Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
256 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 81 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×#14581727 | C2 | semidirect |
| 3. #19127737 | C2 | semidirect |
| 6. #19127473 | C2 | semidirect |
| 7. #344×C83 | C2 | semidirect |
| 11. #14581800 | C4 | semidirect |
| 12. #14581800 | C4 | semidirect |
| 106. C83 | #1814 | semidirect |
| 113. #344 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581800 | 2 |
| C2×#14581727 | 2 |
| #19127737 | 2 |
| #19127719 | 2 |
| #19127717 | 2 |
| #19127473 | 2 |
| #344×C83 | 2 |
| #1814 | 83 |