Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
402 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 161 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. #19127778 | C2 | semidirect |
| 3. #19127774 | C2 | semidirect |
| 4. #19127766 | C2 | semidirect |
| 5. #19127754 | C2 | semidirect |
| 6. #19127666 | C2 | semidirect |
| 7. #432×C83 | C2 | semidirect |
| 93. C83 | #2981 | semidirect |
| 98. #432 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128251 | 2 |
| #19127778 | 2 |
| #19127774 | 2 |
| #19127766 | 2 |
| #19127754 | 2 |
| #19127666 | 2 |
| #432×C83 | 2 |
| #2981 | 83 |