Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
756 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 249 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. #19128468 | C2 | semidirect |
| 3. #19127683 | C2 | semidirect |
| 4. C2×#14581708 | C2 | semidirect |
| 5. #568×C83 | C2 | semidirect |
| 13. C2×#13050574 | C22 | semidirect |
| 14. #14581710 | C22 | semidirect |
| 15. #14581708 | C22 | semidirect |
| 18. C2×M16×C83 | C22 | semidirect |
| 77. C83 | #2888 | semidirect |
| 80. #568 | D83 | semidirect |
| 93. 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×#14581838 | 2 |
| #19128468 | 2 |
| #19127683 | 2 |
| C2×#14581708 | 2 |
| #568×C83 | 2 |
| #2888 | 83 |