Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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. C2×#14581792 | C2 | semidirect |
| 3. #19128095 | C2 | semidirect |
| 4. #19128070 | C2 | semidirect |
| 5. #19127912 | C2 | semidirect |
| 6. #19127907 | C2 | semidirect |
| 7. #19127859 | C2 | semidirect |
| 9. #432×C83 | C2 | semidirect |
| 116. C83 | #3218 | semidirect |
| 125. #432 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581792 | 2 |
| #19128235 | 2 |
| #19128095 | 2 |
| #19128070 | 2 |
| #19127912 | 2 |
| #19127907 | 2 |
| #19127859 | 2 |
| #19127842 | 2 |
| #432×C83 | 2 |
| #3218 | 83 |