Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
162 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 71 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. #19127832 | C2 | semidirect |
| 3. #19127454 | C2 | semidirect |
| 4. Q8⋊(C83⋊C8) | C2 | semidirect |
| 6. #19127422 | C2 | semidirect |
| 55. C8×C83 | M16 | semidirect |
| 78. C83 | #1592 | semidirect |
| 138. C8 | #13050574 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19127832 | 2 |
| #19127779 | 2 |
| #19127454 | 2 |
| Q8⋊(C83⋊C8) | 2 |
| D4⋊(C83⋊C8) | 2 |
| #19127422 | 2 |
| C4×SD16×C83 | 2 |
| #1592 | 83 |