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. C2×#14581798 | C2 | semidirect |
| 2. #19128268 | C2 | semidirect |
| 3. #19127951 | C2 | semidirect |
| 4. #19127934 | C2 | semidirect |
| 5. #19127739 | C2 | semidirect |
| 6. #19127706 | C2 | semidirect |
| 7. C22×D8×C83 | C2 | semidirect |
| 11. C2×#13050573 | C22 | semidirect |
| 12. C2×C8×D83 | C22 | semidirect |
| 15. #14581763 | C22 | semidirect |
| 18. #14581726 | C22 | semidirect |
| 19. #14581724 | C22 | semidirect |
| 20. #14581713 | C22 | semidirect |
| 49. C2×C8×C83 | D4 | semidirect |
| 94. C83 | #3058 | semidirect |
| 95. C22×D8 | D83 | semidirect |
| 139. C2×C8 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581798 | 2 |
| #19128268 | 2 |
| #19127951 | 2 |
| #19127934 | 2 |
| #19127739 | 2 |
| #19127706 | 2 |
| C22×D8×C83 | 2 |
| #3058 | 83 |