Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
274 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 67 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. #19127749 | C2 | semidirect |
| 2. #19127718 | C2 | semidirect |
| 3. #19127706 | C2 | semidirect |
| 4. #19127685 | C2 | semidirect |
| 5. C2×#14581709 | C2 | semidirect |
| 6. #19127473 | C2 | semidirect |
| 111. C83 | #2048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19127749 | 2 |
| #19127718 | 2 |
| #19127706 | 2 |
| #19127685 | 2 |
| C2×#14581709 | 2 |
| #19127473 | 2 |
| C2×AGL(1,ℤ/8)×C83 | 2 |
| #2048 | 83 |