Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
358 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. #19128005 | C2 | semidirect |
| 4. #19127908 | C2 | semidirect |
| 6. #19127806 | C2 | semidirect |
| 7. C4×#13050580 | C2 | semidirect |
| 96. C83 | #3127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128178 | 2 |
| #19128039 | 2 |
| #19128005 | 2 |
| #19127908 | 2 |
| #19127856 | 2 |
| #19127806 | 2 |
| C4×#13050580 | 2 |
| #19127762 | 2 |
| #541×C83 | 2 |
| #3127 | 83 |