Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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×#14581811 | C2 | semidirect |
| 2. C2×#14581798 | C2 | semidirect |
| 3. #19128280 | C2 | semidirect |
| 4. #19127946 | C2 | semidirect |
| 5. #19127945 | C2 | semidirect |
| 6. #19127943 | C2 | semidirect |
| 7. #19127942 | C2 | semidirect |
| 8. #19127934 | C2 | semidirect |
| 9. #107×D83 | C2 | semidirect |
| 10. #19127699 | C2 | semidirect |
| 11. #466×C83 | C2 | semidirect |
| 64. C8×D83 | D4 | semidirect |
| 144. C83 | #3061 | semidirect |
| 153. #466 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581811 | 2 |
| C2×#14581798 | 2 |
| #19128280 | 2 |
| #19127946 | 2 |
| #19127945 | 2 |
| #19127943 | 2 |
| #19127942 | 2 |
| #19127934 | 2 |
| #107×D83 | 2 |
| #19127699 | 2 |
| #466×C83 | 2 |
| #3061 | 83 |