Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
166 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 65 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. #19127828 | C2 | semidirect |
| 4. #19127431 | C2 | semidirect |
| 6. C8×C83⋊C8 | C2 | semidirect |
| 7. #334×C83 | C2 | semidirect |
| 57. C8×C83 | M16 | semidirect |
| 60. C83⋊C8 | SD16 | semidirect |
| 78. C83 | #1590 | semidirect |
| 82. #334 | D83 | semidirect |
| 138. C8 | #13050573 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19127828 | 2 |
| C4×#13050579 | 2 |
| #19127778 | 2 |
| #19127431 | 2 |
| #19127428 | 2 |
| C8×C83⋊C8 | 2 |
| #334×C83 | 2 |
| #1590 | 83 |