Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
338 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 125 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. #19128103 | C2 | semidirect |
| 3. #19128081 | C2 | semidirect |
| 4. #19128070 | C2 | semidirect |
| 7. #19127809 | C2 | semidirect |
| 8. C4×Dic332 | C2 | semidirect |
| 79. C83 | #3177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128313 | 2 |
| #19128103 | 2 |
| #19128081 | 2 |
| #19128070 | 2 |
| #19127959 | 2 |
| #19127942 | 2 |
| #19127809 | 2 |
| C4×Dic332 | 2 |
| #405×C83 | 2 |
| #3177 | 83 |