Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
196 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 17. #108×C83 | C4 | semidirect |
| 69. C83 | #1952 | semidirect |
| 80. #108 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19127743 | 2 |
| C2×#14581726 | 2 |
| #19127656 | 2 |
| #19127469 | 2 |
| C2×#108×C83 | 2 |
| #1952 | 83 |