Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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. #19128053 | C2 | semidirect |
| 4. #19127451 | C2 | semidirect |
| 5. #19127450 | C2 | semidirect |
| 6. #19127446 | C2 | semidirect |
| 76. C83 | #1703 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128053 | 2 |
| #19127981 | 2 |
| #19127779 | 2 |
| #19127451 | 2 |
| #19127450 | 2 |
| #19127446 | 2 |
| #476×C83 | 2 |
| #1703 | 83 |