Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
280 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 97 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×Dic83⋊C8 | C2 | semidirect |
| 5. #19127456 | C2 | semidirect |
| 6. #19127455 | C2 | semidirect |
| 7. C2×#97×C83 | C2 | semidirect |
| 123. C83 | #1924 | semidirect |
| 127. C2×#97 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic83⋊C8 | 2 |
| C2×(C2×D83)⋊C8 | 2 |
| C4×(C2×D83)⋊C4 | 2 |
| #19127456 | 2 |
| #19127455 | 2 |
| C2×#97×C83 | 2 |
| #1924 | 83 |