Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
676 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 181 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. C2×#14581781 | C2 | semidirect |
| 3. #19127618 | C2 | semidirect |
| 4. #19127603 | C2 | semidirect |
| 5. #19127602 | C2 | semidirect |
| 6. C4×C4⋊Dic83 | C2 | semidirect |
| 7. C2×C4×Q8×C83 | C2 | semidirect |
| 39. C2×Q8×C83 | D4 | semidirect |
| 88. C4×C83 | #124 | semidirect |
| 97. C83 | #2548 | semidirect |
| 100. C2×C4×Q8 | D83 | semidirect |
| 124. C2×Q8 | D332 | semidirect |
| 186. C4 | #14581781 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581789 | 2 |
| C2×#14581781 | 2 |
| #19127618 | 2 |
| #19127603 | 2 |
| #19127602 | 2 |
| C4×C4⋊Dic83 | 2 |
| C2×C4×Q8×C83 | 2 |
| #2548 | 83 |