Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
278 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 4. C2×#14581710 | C2 | semidirect |
| 5. #19127606 | C2 | semidirect |
| 6. #19127460 | C2 | semidirect |
| 7. #428×C83 | C2 | semidirect |
| 121. C83 | #2038 | semidirect |
| 123. #428 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128277 | 2 |
| C2×#14581718 | 2 |
| #19127700 | 2 |
| C2×#14581710 | 2 |
| #19127606 | 2 |
| #19127460 | 2 |
| #428×C83 | 2 |
| #2038 | 83 |