Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
418 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19128437 | C2 | semidirect |
| 2. #19128371 | C2 | semidirect |
| 3. #19128089 | C2 | semidirect |
| 4. #19127914 | C2 | semidirect |
| 5. #19127898 | C2 | semidirect |
| 6. #19127894 | C2 | semidirect |
| 7. #19127893 | C2 | semidirect |
| 8. #19127831 | C2 | semidirect |
| 9. #19127813 | C2 | semidirect |
| 10. C4×#13050579 | C2 | semidirect |
| 11. #493×C83 | C2 | semidirect |
| 107. C8×C83 | #41 | semidirect |
| 135. C83 | #3399 | semidirect |
| 139. #493 | D83 | semidirect |
| 243. C8 | #13050589 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128437 | 2 |
| #19128371 | 2 |
| #19128089 | 2 |
| #19127914 | 2 |
| #19127898 | 2 |
| #19127894 | 2 |
| #19127893 | 2 |
| #19127831 | 2 |
| #19127813 | 2 |
| C4×#13050579 | 2 |
| #493×C83 | 2 |
| #3399 | 83 |