Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. Q8×D332 | C2 | semidirect |
| 3. #19128052 | C2 | semidirect |
| 4. #19128045 | C2 | semidirect |
| 5. #19127996 | C2 | semidirect |
| 6. #19127946 | C2 | semidirect |
| 7. #19127906 | C2 | semidirect |
| 8. #19127838 | C2 | semidirect |
| 9. #19127780 | C2 | semidirect |
| 10. #19127708 | C2 | semidirect |
| 11. C4×SD16×C83 | C2 | semidirect |
| 127. C83 | #3329 | semidirect |
| 136. C4×SD16 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128416 | 2 |
| Q8×D332 | 2 |
| #19128052 | 2 |
| #19128045 | 2 |
| #19127996 | 2 |
| #19127946 | 2 |
| #19127906 | 2 |
| #19127838 | 2 |
| #19127780 | 2 |
| #19127708 | 2 |
| C4×SD16×C83 | 2 |
| #3329 | 83 |