Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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. #19127636 | C2 | semidirect |
| 3. #19127621 | C2 | semidirect |
| 5. #19127612 | C2 | semidirect |
| 6. #19127592 | C2 | semidirect |
| 7. #19127569 | C2 | semidirect |
| 8. C2×C4×Q8×C83 | C2 | semidirect |
| 95. C83 | #2632 | semidirect |
| 97. 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×#14581780 | 2 |
| #19127636 | 2 |
| #19127621 | 2 |
| #19127618 | 2 |
| #19127612 | 2 |
| #19127592 | 2 |
| #19127569 | 2 |
| C2×C4×Q8×C83 | 2 |
| #2632 | 83 |