Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
256 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 79 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×#14581723 | C2 | semidirect |
| 5. #19127464 | C2 | semidirect |
| 6. #19127463 | C2 | semidirect |
| 7. #340×C83 | C2 | semidirect |
| 117. C83 | #2077 | semidirect |
| 124. #340 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581723 | 2 |
| C2×(C2×D83)⋊C8 | 2 |
| #19127558 | 2 |
| #19127464 | 2 |
| #19127463 | 2 |
| #340×C83 | 2 |
| #2077 | 83 |