Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
460 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 165 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. #19128034 | C2 | direct (N × H) |
| 3. C2×#14581725 | C2 | semidirect |
| 4. C2×#14581716 | C2 | semidirect |
| 13. #14581725 | C22 | semidirect |
| 14. #14581716 | C22 | semidirect |
| 83. C2×C83 | #484 | semidirect |
| 88. C83 | C2×#484 | semidirect |
| 171. C2 | #19128034 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic83 | 2 |
| #19128034 | 2 |
| C2×#14581725 | 2 |
| C2×#14581716 | 2 |
| C2×C22⋊(C83⋊C8) | 2 |
| C2×C22⋊Q8×C83 | 2 |
| C2×#484 | 83 |