Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
424 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×Q8×Dic83 | C2 | semidirect |
| 3. #19128015 | C2 | semidirect |
| 4. #19128012 | C2 | semidirect |
| 5. #19127994 | C2 | semidirect |
| 6. #19127899 | C2 | semidirect |
| 7. #19127840 | C2 | semidirect |
| 8. #19127804 | C2 | semidirect |
| 9. #19127802 | C2 | semidirect |
| 10. #19127755 | C2 | semidirect |
| 11. #448×C83 | C2 | semidirect |
| 87. Q8×C83 | #41 | semidirect |
| 141. C83 | #3112 | semidirect |
| 149. #448 | D83 | semidirect |
| 229. Q8 | #13050589 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128246 | 2 |
| C2×Q8×Dic83 | 2 |
| #19128015 | 2 |
| #19128012 | 2 |
| #19127994 | 2 |
| #19127899 | 2 |
| #19127840 | 2 |
| #19127804 | 2 |
| #19127802 | 2 |
| #19127755 | 2 |
| #448×C83 | 2 |
| #3112 | 83 |