Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
412 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#14581751 | C2 | semidirect |
| 3. C2×#14581714 | C2 | semidirect |
| 4. #19127464 | C2 | semidirect |
| 5. C2×C22⋊C8×C83 | C2 | semidirect |
| 9. #14581766 | C4 | semidirect |
| 32. C4⋊Dic83 | D4 | semidirect |
| 103. C83 | #1875 | semidirect |
| 107. C2×C22⋊C8 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581766 | 2 |
| C2×#14581751 | 2 |
| C2×#14581714 | 2 |
| #19127464 | 2 |
| C2×C22⋊C8×C83 | 2 |
| #1875 | 83 |