Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
156 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 4. #19127529 | C2 | semidirect |
| 5. #19127528 | C2 | semidirect |
| 6. #19127526 | C2 | semidirect |
| 7. #366×C83 | C2 | semidirect |
| 11. #14581731 | C4 | semidirect |
| 30. C83⋊C16 | C2×C4 | semidirect |
| 34. C16×C83 | C2×C4 | semidirect |
| 64. C83 | #2159 | semidirect |
| 71. #366 | D83 | semidirect |
| 98. C16 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581731 | 2 |
| #19127738 | 2 |
| #107×D83 | 2 |
| #19127529 | 2 |
| #19127528 | 2 |
| #19127526 | 2 |
| #366×C83 | 2 |
| #2159 | 83 |