Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 200 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 |
|---|---|---|
| 1. #19128097 | C2 | semidirect |
| 3. #19127911 | C2 | semidirect |
| 4. #19127447 | C2 | semidirect |
| 5. Q8⋊(C83⋊C8) | C2 | semidirect |
| 89. C83 | #1652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128097 | 2 |
| #19127981 | 2 |
| #19127911 | 2 |
| #19127447 | 2 |
| Q8⋊(C83⋊C8) | 2 |
| D4⋊(C83⋊C8) | 2 |
| #556×C83 | 2 |
| #1652 | 83 |