Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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×Q16×D83 | C2 | semidirect |
| 4. #19127958 | C2 | semidirect |
| 5. #19127957 | C2 | semidirect |
| 6. #19127943 | C2 | semidirect |
| 7. #19127942 | C2 | semidirect |
| 8. #19127939 | C2 | semidirect |
| 9. #19127738 | C2 | semidirect |
| 10. #19127708 | C2 | semidirect |
| 11. #467×C83 | C2 | semidirect |
| 138. C83 | #3059 | semidirect |
| 147. #467 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D83 | 2 |
| C2×#14581798 | 2 |
| #19128274 | 2 |
| #19127958 | 2 |
| #19127957 | 2 |
| #19127943 | 2 |
| #19127942 | 2 |
| #19127939 | 2 |
| #19127738 | 2 |
| #19127708 | 2 |
| #467×C83 | 2 |
| #3059 | 83 |