Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
608 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 197 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×#14581754 | C2 | semidirect |
| 3. #19127812 | C2 | direct (N × H) |
| 4. C2×#14581712 | C2 | semidirect |
| 5. C2×#14581702 | C2 | semidirect |
| 6. C2×#106×C83 | C2 | semidirect |
| 9. C2×D664 | C4 | semidirect |
| 13. #14581754 | C22 | semidirect |
| 16. #14581712 | C22 | semidirect |
| 17. #14581702 | C22 | semidirect |
| 20. #106×C83 | C22 | semidirect |
| 24. C2×D332 | C2×C4 | semidirect |
| 29. D664 | C2×C4 | semidirect |
| 37. C2×C8×C83 | C2×C4 | semidirect |
| 56. D332 | C22×C4 | semidirect |
| 58. C8×C83 | C22×C4 | semidirect |
| 72. C2×C83 | #442 | semidirect |
| 77. C83 | C2×#442 | semidirect |
| 81. C2×#106 | D83 | semidirect |
| 95. #106 | C2×D83 | semidirect |
| 111. C2×C8 | C4×D83 | semidirect |
| 136. C8 | C2×C4×D83 | semidirect |
| 150. C2 | #19127812 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D664 | 2 |
| C2×#14581754 | 2 |
| #19127812 | 2 |
| C2×#14581712 | 2 |
| C2×#14581702 | 2 |
| C2×#106×C83 | 2 |
| C2×#442 | 83 |