Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
228 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 69 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. C2×#14581728 | C2 | semidirect |
| 2. #19127744 | C2 | semidirect |
| 6. #19127469 | C2 | semidirect |
| 7. #424×C83 | C2 | semidirect |
| 98. C83 | #2063 | semidirect |
| 101. #424 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581728 | 2 |
| #19127744 | 2 |
| #19127705 | 2 |
| C2×#14581714 | 2 |
| C2×#14581708 | 2 |
| #19127469 | 2 |
| #424×C83 | 2 |
| #2063 | 83 |