Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
208 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 57 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. #19128073 | C2 | semidirect |
| 2. #19128052 | C2 | semidirect |
| 3. #19128047 | C2 | semidirect |
| 4. #19128047 | C2 | semidirect |
| 5. #19128047 | C2 | semidirect |
| 6. #19127423 | C2 | semidirect |
| 75. C83 | #1717 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128073 | 2 |
| #19128052 | 2 |
| #19128047 | 2 |
| #19127423 | 2 |
| #493×C83 | 2 |
| #1717 | 83 |