Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14581703 | C2 | semidirect |
| 3. C4×C4⋊Dic83 | C2 | semidirect |
| 4. #19127463 | C2 | semidirect |
| 9. #14581713 | C4 | semidirect |
| 15. C4×D4×C83 | C4 | semidirect |
| 22. C2×C83⋊C8 | C2×C4 | semidirect |
| 24. C4⋊Dic83 | C2×C4 | semidirect |
| 50. D4×C83 | C42 | semidirect |
| 91. C83 | #1762 | semidirect |
| 101. C4×D4 | Dic83 | semidirect |
| 141. D4 | C4×Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581713 | 2 |
| C2×#14581703 | 2 |
| C4×C4⋊Dic83 | 2 |
| #19127463 | 2 |
| C2×C4×D4×C83 | 2 |
| #1762 | 83 |