Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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. #19128025 | C2 | semidirect |
| 3. #19128019 | C2 | semidirect |
| 4. #19128014 | C2 | semidirect |
| 5. #19127744 | C2 | semidirect |
| 6. #19127705 | C2 | semidirect |
| 7. #19127665 | C2 | semidirect |
| 8. C2×#117×C83 | C2 | semidirect |
| 18. #14581725 | C22 | semidirect |
| 19. #14581723 | C22 | semidirect |
| 20. #14581712 | C22 | semidirect |
| 21. #14581712 | C22 | semidirect |
| 22. C22⋊(C83⋊C8) | C22 | semidirect |
| 23. C22⋊(C83⋊C8) | C22 | semidirect |
| 28. #117×C83 | C22 | semidirect |
| 29. C2×C4⋊C4×C83 | C22 | semidirect |
| 30. C2×C4⋊C4×C83 | C22 | semidirect |
| 126. C83 | #3094 | semidirect |
| 128. C2×#117 | D83 | semidirect |
| 146. #117 | C2×D83 | semidirect |
| 148. C2×C4⋊C4 | C2×D83 | semidirect |
| 149. C2×C4⋊C4 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581766 | 2 |
| #19128025 | 2 |
| #19128019 | 2 |
| #19128014 | 2 |
| #19127744 | 2 |
| #19127705 | 2 |
| #19127665 | 2 |
| C2×#117×C83 | 2 |
| #3094 | 83 |