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. #19128047 | C2 | semidirect |
| 4. #19128046 | C2 | semidirect |
| 5. #19127992 | C2 | semidirect |
| 6. #19127989 | C2 | semidirect |
| 7. #19127899 | C2 | semidirect |
| 8. #19127825 | C2 | semidirect |
| 9. SD16×Dic83 | C2 | semidirect |
| 10. C4×#13050577 | C2 | semidirect |
| 11. #460×C83 | C2 | semidirect |
| 77. Q8×C83 | #41 | semidirect |
| 99. Dic166 | SD16 | semidirect |
| 126. C83 | #3362 | semidirect |
| 134. #460 | D83 | semidirect |
| 206. Q8 | #13050589 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic166 | 2 |
| #19128371 | 2 |
| #19128047 | 2 |
| #19128046 | 2 |
| #19127992 | 2 |
| #19127989 | 2 |
| #19127899 | 2 |
| #19127825 | 2 |
| SD16×Dic83 | 2 |
| C4×#13050577 | 2 |
| #460×C83 | 2 |
| #3362 | 83 |