Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14581818 | C2 | semidirect |
| 2. #19128251 | C2 | semidirect |
| 3. #19128088 | C2 | semidirect |
| 4. #19128077 | C2 | semidirect |
| 5. #19128073 | C2 | semidirect |
| 6. C4×#13050574 | C2 | semidirect |
| 7. C2×#127×C83 | C2 | semidirect |
| 10. C2×#13050578 | C22 | semidirect |
| 11. C2×#13050575 | C22 | semidirect |
| 13. #14581792 | C22 | semidirect |
| 14. #14581789 | C22 | semidirect |
| 15. #14581780 | C22 | semidirect |
| 18. #14581703 | C22 | semidirect |
| 19. C4×C83⋊C8 | C22 | semidirect |
| 34. #13050574 | D4 | semidirect |
| 71. C83⋊C8 | C2×D4 | semidirect |
| 82. C4×C83 | AGL(1,ℤ/8) | semidirect |
| 91. C83 | #3151 | semidirect |
| 94. C2×#127 | D83 | semidirect |
| 174. C4 | #14581818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581818 | 2 |
| #19128251 | 2 |
| #19128088 | 2 |
| #19128077 | 2 |
| #19128073 | 2 |
| C4×#13050574 | 2 |
| C2×#127×C83 | 2 |
| #3151 | 83 |