Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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×#14581723 | C2 | semidirect |
| 3. C2×#14581712 | C2 | semidirect |
| 4. C2×#14581712 | C2 | semidirect |
| 5. C2×C22⋊(C83⋊C8) | C2 | semidirect |
| 6. #19127463 | C2 | semidirect |
| 7. #380×C83 | C2 | semidirect |
| 41. C2×C83⋊C8 | D4 | semidirect |
| 144. C83 | #2034 | semidirect |
| 150. #380 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581766 | 2 |
| C2×#14581723 | 2 |
| C2×#14581712 | 2 |
| C2×C22⋊(C83⋊C8) | 2 |
| #19127463 | 2 |
| #380×C83 | 2 |
| #2034 | 83 |