Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
510 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 99 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. C22×D664 | C2 | semidirect |
| 2. C2×#14581789 | C2 | semidirect |
| 3. C2×#14581714 | C2 | semidirect |
| 4. #19127603 | C2 | semidirect |
| 5. #336×C83 | C2 | semidirect |
| 32. C2×D332 | D4 | semidirect |
| 41. C2×C8×C83 | D4 | semidirect |
| 56. C2×C4×C83 | D8 | semidirect |
| 98. C83 | #2011 | semidirect |
| 103. #336 | D83 | semidirect |
| 137. C2×C8 | D332 | semidirect |
| 163. C2×C4 | D664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D664 | 2 |
| C2×#14581789 | 2 |
| C2×#14581714 | 2 |
| #19127603 | 2 |
| #336×C83 | 2 |
| #2011 | 83 |