Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
354 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 354 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 |
|---|---|---|
| 2. #19128408 | C2 | semidirect |
| 3. #19128106 | C2 | semidirect |
| 4. #19128043 | C2 | semidirect |
| 5. #19128015 | C2 | semidirect |
| 6. #19127997 | C2 | semidirect |
| 7. #19127992 | C2 | semidirect |
| 8. #19127947 | C2 | semidirect |
| 9. C4×#13050579 | C2 | semidirect |
| 10. #19127743 | C2 | semidirect |
| 11. #436×C83 | C2 | semidirect |
| 122. C83 | #3357 | semidirect |
| 132. #436 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128416 | 2 |
| #19128408 | 2 |
| #19128106 | 2 |
| #19128043 | 2 |
| #19128015 | 2 |
| #19127997 | 2 |
| #19127992 | 2 |
| #19127947 | 2 |
| C4×#13050579 | 2 |
| #19127743 | 2 |
| #436×C83 | 2 |
| #3357 | 83 |