Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
582 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#14581786 | C2 | semidirect |
| 2. #19127592 | C2 | semidirect |
| 3. #19127585 | C2 | semidirect |
| 5. #19127574 | C2 | semidirect |
| 6. #19127569 | C2 | semidirect |
| 7. C22×C42×C83 | C2 | semidirect |
| 40. C42×C83 | D4 | semidirect |
| 65. C22×C83 | #126 | semidirect |
| 83. C83 | #2852 | semidirect |
| 85. C22×C42 | D83 | semidirect |
| 123. C42 | C22⋊D83 | semidirect |
| 151. C22 | #14581786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581786 | 2 |
| #19127592 | 2 |
| #19127585 | 2 |
| #19127580 | 2 |
| #19127574 | 2 |
| #19127569 | 2 |
| C22×C42×C83 | 2 |
| #2852 | 83 |