Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 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 |
|---|---|---|
| 2. C2×#14581750 | C2 | semidirect |
| 3. #19128023 | C2 | direct (N × H) |
| 4. C2×#14581726 | C2 | semidirect |
| 5. C2×#14581723 | C2 | semidirect |
| 6. C2×#14581713 | C2 | semidirect |
| 7. C2×(C2×D83)⋊C8 | C2 | semidirect |
| 8. C2×#102×C83 | C2 | semidirect |
| 15. #14581750 | C22 | semidirect |
| 21. #14581726 | C22 | semidirect |
| 22. #14581723 | C22 | semidirect |
| 23. #14581713 | C22 | semidirect |
| 24. (C2×D83)⋊C8 | C22 | semidirect |
| 28. #102×C83 | C22 | semidirect |
| 109. C2×C83 | #482 | semidirect |
| 115. C83 | C2×#482 | semidirect |
| 122. C2×#102 | D83 | semidirect |
| 142. #102 | C2×D83 | semidirect |
| 225. C2 | #19128023 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581763 | 2 |
| C2×#14581750 | 2 |
| #19128023 | 2 |
| C2×#14581726 | 2 |
| C2×#14581723 | 2 |
| C2×#14581713 | 2 |
| C2×(C2×D83)⋊C8 | 2 |
| C2×#102×C83 | 2 |
| C2×#482 | 83 |