Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. #19127623 | C2 | semidirect |
| 4. #19127612 | C2 | semidirect |
| 5. #19127608 | C2 | semidirect |
| 6. #19127592 | C2 | semidirect |
| 7. #19127591 | C2 | semidirect |
| 8. #19127582 | C2 | semidirect |
| 9. C2×C4⋊Q8×C83 | C2 | semidirect |
| 126. C83 | #2731 | semidirect |
| 127. C2×C4⋊Q8 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581781 | 2 |
| #19127623 | 2 |
| #19127618 | 2 |
| #19127612 | 2 |
| #19127608 | 2 |
| #19127592 | 2 |
| #19127591 | 2 |
| #19127582 | 2 |
| C2×C4⋊Q8×C83 | 2 |
| #2731 | 83 |