Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
296 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 9. C4⋊(C83⋊C8) | C4 | semidirect |
| 15. C4×C8×C83 | C4 | semidirect |
| 20. C4⋊Dic83 | C8 | direct (N × H) |
| 49. C8×C83 | C4⋊C4 | semidirect |
| 57. C4×C83 | C4×C8 | semidirect |
| 69. C83 | C8×C4⋊C4 | semidirect |
| 83. C4×C8 | Dic83 | semidirect |
| 119. C8 | C4⋊Dic83 | direct (N × H) |
| 127. C4 | C8×Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C83⋊C8) | 2 |
| C2×C8×Dic83 | 2 |
| C4×C4⋊Dic83 | 2 |
| #19127455 | 2 |
| C2×C4×C8×C83 | 2 |
| C8×C4⋊C4 | 83 |