Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 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. #19128104 | C2 | semidirect |
| 4. #19127453 | C2 | semidirect |
| 5. #19127448 | C2 | semidirect |
| 6. #19127447 | C2 | semidirect |
| 61. C83⋊C8 | SD16 | semidirect |
| 79. C83 | #1673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128104 | 2 |
| #19127906 | 2 |
| D4×C83⋊C8 | 2 |
| #19127453 | 2 |
| #19127448 | 2 |
| #19127447 | 2 |
| #461×C83 | 2 |
| #1673 | 83 |