Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 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 |
|---|---|---|
| 2. #19127618 | C2 | semidirect |
| 3. #19127602 | C2 | semidirect |
| 4. #19127547 | C2 | semidirect |
| 5. C2×#125×C83 | C2 | semidirect |
| 59. C83 | #2641 | semidirect |
| 61. C2×#125 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581789 | 2 |
| #19127618 | 2 |
| #19127602 | 2 |
| #19127547 | 2 |
| C2×#125×C83 | 2 |
| #2641 | 83 |