Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
348 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 181 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. #19127830 | C2 | semidirect |
| 3. #19127828 | C2 | semidirect |
| 33. C2×C83⋊C8 | Q8 | semidirect |
| 84. C83 | #2961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128254 | 2 |
| #19127830 | 2 |
| #19127828 | 2 |
| #19127727 | 2 |
| #19127724 | 2 |
| #19127659 | 2 |
| #19127657 | 2 |
| C2×#14581702 | 2 |
| #424×C83 | 2 |
| #2961 | 83 |