Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 2. #19128430 | C2 | semidirect |
| 3. #19128054 | C2 | semidirect |
| 5. #19128003 | C2 | semidirect |
| 6. #19127987 | C2 | semidirect |
| 7. #19127921 | C2 | semidirect |
| 8. #19127825 | C2 | semidirect |
| 9. C4×#13050580 | C2 | semidirect |
| 10. SD16×Dic83 | C2 | semidirect |
| 118. C83 | #3365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128437 | 2 |
| #19128430 | 2 |
| #19128054 | 2 |
| #19128047 | 2 |
| #19128003 | 2 |
| #19127987 | 2 |
| #19127921 | 2 |
| #19127825 | 2 |
| C4×#13050580 | 2 |
| SD16×Dic83 | 2 |
| #460×C83 | 2 |
| #3365 | 83 |