Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 141 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×D664 | C2 | semidirect |
| 2. C2×#14581798 | C2 | semidirect |
| 3. #19128270 | C2 | semidirect |
| 4. #19127955 | C2 | semidirect |
| 5. #19127938 | C2 | semidirect |
| 6. #19127705 | C2 | semidirect |
| 7. #427×C83 | C2 | semidirect |
| 15. C2×#13050573 | C22 | semidirect |
| 16. C2×C8×D83 | C22 | semidirect |
| 19. #14581767 | C22 | semidirect |
| 21. #14581712 | C22 | semidirect |
| 24. #107×C83 | C22 | semidirect |
| 25. #106×C83 | C22 | semidirect |
| 46. C2×C8×C83 | D4 | semidirect |
| 94. C83 | #3058 | semidirect |
| 100. #427 | D83 | semidirect |
| 117. #107 | C2×D83 | semidirect |
| 118. #106 | C2×D83 | semidirect |
| 139. C2×C8 | D332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D664 | 2 |
| C2×#14581798 | 2 |
| #19128270 | 2 |
| #19127955 | 2 |
| #19127938 | 2 |
| #19127705 | 2 |
| #427×C83 | 2 |
| #3058 | 83 |