Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
474 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 95 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. C22×#13050577 | C2 | semidirect |
| 3. C2×#14581714 | C2 | semidirect |
| 4. C2×#14581713 | C2 | semidirect |
| 5. #19127608 | C2 | semidirect |
| 6. #19127455 | C2 | semidirect |
| 7. C22×SD16×C83 | C2 | semidirect |
| 42. C2×C83⋊C8 | D4 | semidirect |
| 53. C2×Q8×C83 | D4 | semidirect |
| 65. C2×C8×C83 | D4 | semidirect |
| 99. C2×Dic83 | SD16 | semidirect |
| 136. C83 | #2014 | semidirect |
| 138. C22×SD16 | D83 | semidirect |
| 170. C2×Q8 | C22⋊D83 | semidirect |
| 197. C2×C8 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13050577 | 2 |
| C2×#14581788 | 2 |
| C2×#14581714 | 2 |
| C2×#14581713 | 2 |
| #19127608 | 2 |
| #19127455 | 2 |
| C22×SD16×C83 | 2 |
| #2014 | 83 |