Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
338 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 2. #19128100 | C2 | semidirect |
| 3. #19128080 | C2 | semidirect |
| 4. #19128071 | C2 | semidirect |
| 5. #19128069 | C2 | semidirect |
| 8. #19127806 | C2 | semidirect |
| 9. C4×#13050580 | C2 | semidirect |
| 103. C83 | #3177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128313 | 2 |
| #19128100 | 2 |
| #19128080 | 2 |
| #19128071 | 2 |
| #19128069 | 2 |
| #19127957 | 2 |
| #19127940 | 2 |
| #19127806 | 2 |
| C4×#13050580 | 2 |
| #19127657 | 2 |
| #541×C83 | 2 |
| #3177 | 83 |