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 |
|---|---|---|
| 3. #19127453 | C2 | semidirect |
| 4. Q8⋊(C83⋊C8) | C2 | semidirect |
| 6. #19127423 | C2 | semidirect |
| 7. C8×Q8×C83 | C2 | semidirect |
| 43. Q8×C83 | M16 | semidirect |
| 78. C83 | #1588 | semidirect |
| 79. C8×Q8 | D83 | semidirect |
| 121. Q8 | #13050573 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13050577 | 2 |
| #19127780 | 2 |
| #19127453 | 2 |
| Q8⋊(C83⋊C8) | 2 |
| #19127428 | 2 |
| #19127423 | 2 |
| C8×Q8×C83 | 2 |
| #1588 | 83 |