Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
390 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 91 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. C22×#13050580 | C2 | semidirect |
| 3. C2×#14581716 | C2 | semidirect |
| 5. #19127607 | C2 | semidirect |
| 6. #19127456 | C2 | semidirect |
| 126. C83 | #2015 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13050580 | 2 |
| C22×#13050578 | 2 |
| C2×#14581716 | 2 |
| C2×#14581713 | 2 |
| #19127607 | 2 |
| #19127456 | 2 |
| C2×#124×C83 | 2 |
| #2015 | 83 |