Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #19128258 | C2 | semidirect |
| 3. #19128061 | C2 | semidirect |
| 4. #19128056 | C2 | semidirect |
| 5. #19127711 | C2 | semidirect |
| 7. C4×M16×C83 | C2 | semidirect |
| 10. #14581792 | C22 | semidirect |
| 11. #14581784 | C22 | semidirect |
| 19. #14581717 | C22 | semidirect |
| 23. #97×C83 | C22 | semidirect |
| 24. C4×C8×C83 | C22 | semidirect |
| 84. C83 | #3140 | semidirect |
| 91. C4×M16 | D83 | semidirect |
| 107. #97 | C2×D83 | semidirect |
| 108. C4×C8 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128258 | 2 |
| C2×#14581780 | 2 |
| #19128061 | 2 |
| #19128056 | 2 |
| #19127711 | 2 |
| #19127707 | 2 |
| C4×M16×C83 | 2 |
| #3140 | 83 |