Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
392 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 123 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. #19128431 | C2 | semidirect |
| 3. #19128046 | C2 | semidirect |
| 4. #19127989 | C2 | semidirect |
| 5. #19127988 | C2 | semidirect |
| 6. #19127900 | C2 | semidirect |
| 7. #19127898 | C2 | semidirect |
| 8. C8×Dic166 | C2 | semidirect |
| 9. #19127792 | C2 | semidirect |
| 10. C4×#13050579 | C2 | semidirect |
| 11. #486×C83 | C2 | semidirect |
| 98. Dic166 | SD16 | semidirect |
| 99. Dic166 | #41 | semidirect |
| 126. C83 | #3362 | semidirect |
| 130. #486 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128431 | 2 |
| #19128371 | 2 |
| #19128046 | 2 |
| #19127989 | 2 |
| #19127988 | 2 |
| #19127900 | 2 |
| #19127898 | 2 |
| C8×Dic166 | 2 |
| #19127792 | 2 |
| C4×#13050579 | 2 |
| #486×C83 | 2 |
| #3362 | 83 |