Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
484 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 255 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 |
|---|---|---|
| 3. #19127729 | C2 | semidirect |
| 4. #19127727 | C2 | semidirect |
| 5. #19127724 | C2 | semidirect |
| 6. C2×Dic83⋊C8 | C2 | semidirect |
| 75. Dic83 | #131 | semidirect |
| 81. C83 | #2906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581799 | 2 |
| #41×Dic83 | 2 |
| #19127729 | 2 |
| #19127727 | 2 |
| #19127724 | 2 |
| C2×Dic83⋊C8 | 2 |
| C2×#131×C83 | 2 |
| #2906 | 83 |