Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
340 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. #19128105 | C2 | semidirect |
| 3. #19128045 | C2 | semidirect |
| 4. #19128042 | C2 | semidirect |
| 5. #19127985 | C2 | semidirect |
| 6. #19127943 | C2 | semidirect |
| 7. #19127942 | C2 | semidirect |
| 8. #19127795 | C2 | semidirect |
| 10. #19127738 | C2 | semidirect |
| 11. #427×C83 | C2 | semidirect |
| 115. C83 | #3342 | semidirect |
| 126. #427 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128419 | 2 |
| #19128105 | 2 |
| #19128045 | 2 |
| #19128042 | 2 |
| #19127985 | 2 |
| #19127943 | 2 |
| #19127942 | 2 |
| #19127795 | 2 |
| C8×C22⋊D83 | 2 |
| #19127738 | 2 |
| #427×C83 | 2 |
| #3342 | 83 |