Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
344 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 113 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×#14581716 | C2 | semidirect |
| 3. C2×#14581703 | C2 | semidirect |
| 4. #19127571 | C2 | semidirect |
| 15. #124×C83 | C4 | semidirect |
| 85. C83 | #1959 | semidirect |
| 95. #124 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581716 | 2 |
| C2×#14581713 | 2 |
| C2×#14581703 | 2 |
| #19127571 | 2 |
| C2×#124×C83 | 2 |
| #1959 | 83 |