Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 117 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×#14581715 | C2 | semidirect |
| 3. C2×#14581712 | C2 | semidirect |
| 4. C2×C22⋊(C83⋊C8) | C2 | semidirect |
| 5. #380×C83 | C2 | semidirect |
| 9. C2×#13050590 | C4 | semidirect |
| 81. D332 | C22⋊C4 | semidirect |
| 85. Dic166 | C22⋊C4 | semidirect |
| 116. C83 | #1788 | semidirect |
| 121. #380 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13050590 | 2 |
| C2×#14581715 | 2 |
| C2×#14581712 | 2 |
| C2×C22⋊(C83⋊C8) | 2 |
| #380×C83 | 2 |
| #1788 | 83 |