Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
208 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 57 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. #19128053 | C2 | semidirect |
| 3. #19127983 | C2 | semidirect |
| 4. #19127449 | C2 | semidirect |
| 5. #19127431 | C2 | semidirect |
| 89. C83 | #1643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128408 | 2 |
| #19128053 | 2 |
| #19127983 | 2 |
| #19127449 | 2 |
| #19127431 | 2 |
| D4⋊(C83⋊C8) | 2 |
| #461×C83 | 2 |
| #1643 | 83 |