Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
340 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 340 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. #19128426 | C2 | semidirect |
| 3. #19128068 | C2 | semidirect |
| 4. #19128051 | C2 | semidirect |
| 5. #19128010 | C2 | semidirect |
| 6. #19127997 | C2 | semidirect |
| 8. #19127828 | C2 | semidirect |
| 117. C83 | #3372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128426 | 2 |
| #19128408 | 2 |
| #19128068 | 2 |
| #19128051 | 2 |
| #19128010 | 2 |
| #19127997 | 2 |
| #19127904 | 2 |
| #19127828 | 2 |
| #19127802 | 2 |
| C4×#13050578 | 2 |
| #461×C83 | 2 |
| #3372 | 83 |