Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 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. #19128258 | C2 | semidirect |
| 3. #19128074 | C2 | semidirect |
| 4. #19128048 | C2 | semidirect |
| 5. #19127902 | C2 | semidirect |
| 6. #19127854 | C2 | semidirect |
| 7. #431×C83 | C2 | semidirect |
| 11. C2×#13050579 | C22 | semidirect |
| 12. #14581792 | C22 | semidirect |
| 13. #14581792 | C22 | semidirect |
| 22. C4×Dic166 | C22 | semidirect |
| 24. #14581714 | C22 | semidirect |
| 26. C4⋊C8×C83 | C22 | semidirect |
| 28. C4×C8×C83 | C22 | semidirect |
| 65. C2×C4×C83 | SD16 | semidirect |
| 105. C83 | #3208 | semidirect |
| 112. #431 | D83 | semidirect |
| 130. C4⋊C8 | C2×D83 | semidirect |
| 133. C4×C8 | C2×D83 | semidirect |
| 180. C2×C4 | #13050579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128258 | 2 |
| C2×#14581789 | 2 |
| #19128074 | 2 |
| #19128048 | 2 |
| #19127902 | 2 |
| #19127854 | 2 |
| #431×C83 | 2 |
| #3208 | 83 |