Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
708 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 708 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 |
|---|---|---|
| 1. C2×#14581775 | C2 | semidirect |
| 3. #19127636 | C2 | semidirect |
| 4. #19127602 | C2 | semidirect |
| 5. #19127570 | C2 | semidirect |
| 6. C4×C22⋊Dic83 | C2 | semidirect |
| 7. C22×C4⋊C4×C83 | C2 | semidirect |
| 33. C22⋊Dic83 | D4 | semidirect |
| 85. C4×C83 | #123 | semidirect |
| 95. C83 | #2501 | semidirect |
| 98. C22×C4⋊C4 | D83 | semidirect |
| 182. C4 | #14581775 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581775 | 2 |
| C2×#14581766 | 2 |
| #19127636 | 2 |
| #19127602 | 2 |
| #19127570 | 2 |
| C4×C22⋊Dic83 | 2 |
| C22×C4⋊C4×C83 | 2 |
| #2501 | 83 |