Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 1. Q8×Dic166 | C2 | semidirect |
| 3. #19128048 | C2 | semidirect |
| 4. #19128046 | C2 | semidirect |
| 5. #19127991 | C2 | semidirect |
| 6. #19127990 | C2 | semidirect |
| 7. #19127901 | C2 | semidirect |
| 8. #19127899 | C2 | semidirect |
| 9. C8×Dic166 | C2 | semidirect |
| 10. #19127786 | C2 | semidirect |
| 11. C4×SD16×C83 | C2 | semidirect |
| 77. Q8×C83 | #41 | semidirect |
| 99. Dic166 | SD16 | semidirect |
| 126. C83 | #3362 | semidirect |
| 137. C4×SD16 | D83 | semidirect |
| 206. Q8 | #13050590 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic166 | 2 |
| #19128372 | 2 |
| #19128048 | 2 |
| #19128046 | 2 |
| #19127991 | 2 |
| #19127990 | 2 |
| #19127901 | 2 |
| #19127899 | 2 |
| C8×Dic166 | 2 |
| #19127786 | 2 |
| C4×SD16×C83 | 2 |
| #3362 | 83 |