Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
282 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 67 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×#14581727 | C2 | semidirect |
| 3. #19127700 | C2 | semidirect |
| 4. C2×#14581712 | C2 | semidirect |
| 5. C2×#14581708 | C2 | semidirect |
| 6. #19127669 | C2 | semidirect |
| 7. #343×C83 | C2 | semidirect |
| 117. C83 | #2051 | semidirect |
| 124. #343 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581820 | 2 |
| C2×#14581727 | 2 |
| #19127700 | 2 |
| C2×#14581712 | 2 |
| C2×#14581708 | 2 |
| #19127669 | 2 |
| #343×C83 | 2 |
| #2051 | 83 |