Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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×#14581813 | C2 | semidirect |
| 2. #19128252 | C2 | semidirect |
| 3. C4×#13050589 | C2 | semidirect |
| 4. #19127926 | C2 | semidirect |
| 5. #19127918 | C2 | semidirect |
| 6. #19127908 | C2 | semidirect |
| 7. #19127902 | C2 | semidirect |
| 8. #19127896 | C2 | semidirect |
| 9. C4⋊C8×D83 | C2 | semidirect |
| 10. #19127696 | C2 | semidirect |
| 11. #461×C83 | C2 | semidirect |
| 47. #13050589 | D4 | semidirect |
| 136. C4×C83 | #135 | semidirect |
| 151. C83 | #3035 | semidirect |
| 158. #461 | D83 | semidirect |
| 292. C4 | #14581813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581813 | 2 |
| #19128252 | 2 |
| C4×#13050589 | 2 |
| #19127926 | 2 |
| #19127918 | 2 |
| #19127908 | 2 |
| #19127902 | 2 |
| #19127896 | 2 |
| C4⋊C8×D83 | 2 |
| #19127696 | 2 |
| #461×C83 | 2 |
| #3035 | 83 |