Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
480 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. C2×#14581790 | C2 | semidirect |
| 5. #19127910 | C2 | semidirect |
| 6. #19127905 | C2 | semidirect |
| 7. #19127724 | C2 | semidirect |
| 8. #19127709 | C2 | semidirect |
| 9. #419×C83 | C2 | semidirect |
| 116. Dic83 | #137 | semidirect |
| 122. C83 | #3039 | semidirect |
| 131. #419 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581825 | 2 |
| C2×#14581823 | 2 |
| C2×#14581790 | 2 |
| #19128169 | 2 |
| #19127910 | 2 |
| #19127905 | 2 |
| #19127724 | 2 |
| #19127709 | 2 |
| #419×C83 | 2 |
| #3039 | 83 |