Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
434 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 121 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. #19128249 | C2 | semidirect |
| 2. C4×#13050591 | C2 | semidirect |
| 3. #19128024 | C2 | semidirect |
| 4. #19127996 | C2 | semidirect |
| 5. #19127992 | C2 | semidirect |
| 6. #19127893 | C2 | semidirect |
| 7. #19127845 | C2 | semidirect |
| 8. SD16×Dic83 | C2 | semidirect |
| 9. #19127781 | C2 | semidirect |
| 10. #19127753 | C2 | semidirect |
| 11. #460×C83 | C2 | semidirect |
| 87. Q8×C83 | #41 | semidirect |
| 106. D332 | #41 | semidirect |
| 145. C83 | #3106 | semidirect |
| 151. #460 | D83 | semidirect |
| 233. Q8 | #13050589 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128249 | 2 |
| C4×#13050591 | 2 |
| #19128024 | 2 |
| #19127996 | 2 |
| #19127992 | 2 |
| #19127893 | 2 |
| #19127845 | 2 |
| SD16×Dic83 | 2 |
| #19127781 | 2 |
| #19127753 | 2 |
| #460×C83 | 2 |
| #3106 | 83 |