Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. C2×#14581821 | C2 | semidirect |
| 2. Q8×D332 | C2 | semidirect |
| 4. #19128081 | C2 | semidirect |
| 5. #19127960 | C2 | semidirect |
| 6. #19127911 | C2 | semidirect |
| 7. #19127906 | C2 | semidirect |
| 8. #19127864 | C2 | semidirect |
| 9. #19127858 | C2 | semidirect |
| 10. #19127780 | C2 | semidirect |
| 11. C4×SD16×C83 | C2 | semidirect |
| 73. SD16×C83 | D4 | semidirect |
| 123. C4×C83 | #137 | semidirect |
| 135. C83 | #3276 | semidirect |
| 145. C4×SD16 | D83 | semidirect |
| 196. SD16 | D332 | semidirect |
| 261. C4 | #14581821 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581821 | 2 |
| Q8×D332 | 2 |
| #19128355 | 2 |
| #19128081 | 2 |
| #19127960 | 2 |
| #19127911 | 2 |
| #19127906 | 2 |
| #19127864 | 2 |
| #19127858 | 2 |
| #19127780 | 2 |
| C4×SD16×C83 | 2 |
| #3276 | 83 |